Algebra, General Topology

• Applications of formal languages, automata, and codes (cb)
• Computational geometry and algebra (cybsec)
• Theory of formal languages, automata and codes (cybsec)

Books and Lecture Notes

I. I. Guran, and O. V. Gutik,Mathematics for Economists. For Students of Departments of International Relations. Lecture Notes. Znannya, Kyiv, 2008, 388 pp. (in Ukrainian).

Scientific Papers

1994:

O. V. Gutik, Embedding of topological semigroups into simple semigroups, Mat. Stud. 3 (1994),10-14, (in Russian) (MR 1692849 (2000m:22006), Zbl 0928.22004).

1996:

O. V. Gutik, Any topological semigroup topologically isomorphically embeds into a simple path-connected topological semigroup, Algebra and Topology, Lviv Univ. Press (1996), 65-73, (in Ukrainian).

O. V. Gutik, On the structure of the band of a compact inverse semigroup with open translations, Mat. Stud. 6 (1996), 33-38, (in Russian) (MR 1691120 (2000a:22003), Zbl 0928.22005).

O. V. Gutik, Embeddings of Topological Inverse Semigroups and the Structure of their Bands with Restrictions on Translations, Dissertation, Lviv State Univ. (1996) 96pp.

1997:

O. V. Gutik, On a coarsening of a direct sum topology on the Bruck semigroup, Visn. L’viv. Univ., Ser. Mekh.-Mat. 47 (1997), 17-21, (in Ukrainian).

1998:

O. V. Gutik, Embedding of countable topological semigroups into simple countable connected topolological semigroups, Mat. Metody Fiz.-Mekh. Polya 41 (1998), no. 3, 16-21 (in Ukrainian). English Version in: J. Math. Sci. 104 (2001), no. 5, 1422-1427 (doi:10.1023/A:1011311030702, MR 1706772 (2000e:22002), Zbl 0933.22004).

1999:

O. V. Gutik, On compact semilattices with open principal filters, Mat. Metody Fiz.-Mekh. Polya 42 (1999), no. 3, 91-94, (in Ukrainian) (MR 1977866 (2004c:06009), Zbl 1050.54519).

O. V. Gutik, On Howie semigroup, Mat. Metody Fiz.-Mekh. Polya 42 (1999), no. 4, 127-132, (in Ukrainian) (MR 1967818, Zbl 1047.22500).

2000:

O. V. Gutik, Ye. G. Zelenyuk, On non-proper homomorphisms of the semigroups of ultrafiltres, Mat. Metody Fiz.-Mekh. Polya 43 (2000), no. 1, 19-22, (in Ukrainian) (MR 1972601 (2004b:22006), Zbl 1054.22002).

O. Gutik, Compact topological inverse semigroups, Semigroup Forum 60 (2000), no. 2, 243-252 (doi: 10.1007/s002339910017, MR 1830131 (2002e:22004), Zbl 0945.22002).

O. V. Gutik, On homomorphisms of topological inverse semigroups, Mat. Metody Fiz.-Mekh. Polya 43 (2000), no. 2, 75-82, (in Ukrainian) (MR 1977836 (2004a:22001), Zbl 1052.54512).

2001:

O. V. Gutik, and K. P. Pavlyk, The H-closedness of topological inverse semigroups and topological Brandt λ-extensions, XVI Open Scientific and Technical Conference of Young Scientists of the Karpenko Physico-Mechanical Institute of NASU. May 17-18, 2001. Lviv, Ukraine. Proceedings. (2001), 240-243.

O. V. Gutik, and K. P. Pavlyk, Minimal topologies on semigroups of matrix units, International Scientific and Technical Conference “Information of processes of formation of open systems on basis DBMS, design computer-aided …”. June 26-28, 2001. Vologda, Russia. Proceedings. (2001), 301-305.

T. O. Banakh, I. Yo. Guran, and O. V. Gutik, Free topological inverse semigroups, Mat. Stud.15 (2001), no. 1, 23-43 (MR 1871924 (2003e:20072), Zbl 0990.22001).

O. V. Gutik, and K. P. Pavlyk, H-closed topological semigroups and topological Brandt λ-extensions, Mat. Metody Fiz.-Mekh. Polya 44 (2001), no. 3, 20-28, (in Ukrainian) (MR 1967909 (2004a:22002), Zbl 1098.22500).

2002:

O. V. Gutik, M. Radjagopalan, and K. Sundaresan, Compact semilattices with open principal filters, J. Austral. Math. Soc. 72, №3 (2002), 349-362 (doi: 10.1017/S1446788700036776, MR 1902205 (2003f:22005), Zbl 1024.22001).

O. V. Gutik, and K. P. Pavlyk, Embedding of topological semigroups, Mat. Metody Fiz.-Mekh. Polya 45 (2002), no. 1, 90-96, (in Ukrainian) (MR 1967652 (2003m:22005), Zbl 1073.54017).

I. Yo. Guran, and O. V. Gutik, The bicyclic semigroup and countably compact topological inverse semigroups, XVII Open Scientific and Technical Conference of Young Scientists of the Karpenko Physic and Mechanics Institute of NASU. May 15-17, 2002. Lviv, Ukraine. Proceedings. (2002), 149-152.

T. O, Banach, and O. V. Gutik, On a counterpart of Franklin Theorem for topological semigroups, XVII Open Scientific and Technical Conference of Young Scientists of the Karpenko Physico-Mechanical Institute of NASU. May 15-17, 2002. Lviv, Ukraine. Proceedings. (2002), 153-155.

2003:

O. Gutik, and K. Pavlyk, Topological Brandt λ-extensions of absolutely H-closed topological inverse semigroups, Visn. L’viv. Univ., Ser. Mekh.-Mat. 61 (2003), 98-105 (Zbl 1034.22003).

O. V. Gutik, and O. Ye. Lebidko, On semigroup of compact subsets of a paratopological group, Applied Problems of Mech. and Math. 1 (2003), 20-24.

2004:

O. V. Gutik, and K. P. Pavlyk, On 0-simple initially τ-compact topological inverse semigroups, Conference of Young Scientists on Modern Problems in Mechanics and Mathematics, Lviv, May 24-26, 2004. Proceedings, Lviv (2004) 179-181.

T. O. Banakh, and O. V. Gutik, On the continuity of inversion in countably compact inverse topological semigroups, Semigroup Forum 68 (2004), no. 3, 411-418 (doi: 10.1007/s00233-003-0023-y, MR 2050899 (2005c:22005), Zbl 1052.22003).

2005:

O. V. Gutik, and K. P. Pavlyk, Topological semigroups of matrix units, Algebra Discr. Math. no. 3 (2005), 1-17 (MR 2237891 (2007e:20125), Zbl 1092.22002).

T. Banakh, O. V. Gutik, and M. Rajagopalan, Compatible algebraic structures on scattered compacta, Topology Appl., 153 (2005), no. 5-6, 710-723 (doi: 10.1016/j.topol.2005.01.004, MR 2201483 (2006k:54048), Zbl 1087.22003).

O. V. Gutik, Yu. M. Livach, Embediins of topological semigroups into nilpotent-generated semigroups, Mat. Metody Fiz.-Mekh. Polya 48 (2005), no. 4, 66-77 (in Ukrainian), (MR 2229292 (2007b:20122), Zbl 1110.20045).

O. V. Gutik, and K. P. Pavlyk, On topological semigroups of matrix units, Semigroup Forum 71 (2005), no. 3, 389-400 (doi: 10.1007/s00233-005-0530-0, MR 2204758 (2006m:22003), Zbl 1092.22003).

2006:

O. V. Gutik, and K. P. Pavlyk, On Brandt λ⁰-extensions of semigroups with zero, Mat. Metody Fiz.-Mekh. Polya 49 (2006), no. 3, 26-40 (MR 2255060 (2007i:22005), Zbl 1126.22301).

2007:

I. Chuchman, and O. Gutik, On H-closed topological semigroups and semilattices, Algebra Discr. Math. (2007), no. 1, 13-23 (MR2367511 (2008j:22003), Zbl 1164.06332).

O. Gutik, and D. Repovš, On 0-simple countably compact topological inverse semigroups, Semigroup Forum 75 (2007), no. 2, 464-469 (doi: 10.1007/s00233-007-0706-x, MR2350768 (2008g:22001), Zbl 1140.22001, arXiv:0804.1437).

2008:

O. Gutik, and D. Repovš, On linearly ordered H-closed topological semilattices, Semigroup Forum 77 (2008), no. 3, 474-481 (doi: 10.1007/s00233-008-9102-4, MR2457332 (2009i:54063), Zbl 1166.22003, arXiv:0804.1438).

2009:

O. Gutik, J. Lawson, and D. Repovš, Semigroup closures of finite rank symmetric inverse semigroups, Semigroup Forum 78 (2009), no. 2, 326-336 (doi: 10.1007/s00233-008-9112-2, MR2486644 (2010f:20066), Zbl 1165.22002, arXiv:0804.1439).

T. Banakh, S. Dimitrova, and O. Gutik, The Rees-Suschkewitsch Theorem for simple topological semigroups, Mat. Stud. 31 (2009), no. 2, 211-218 (MR2643478 (2011c:22003), Zbl 1199.22004, arXiv:0811.1371).

O. Gutik, D. Pagon, and D. Repovš, The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups, Acta Math. Hungar. 124 (2009), no. 3, 201-214 (doi: 10.1007/s10474-009-8144-8, MR2525561 (2010d:22002), Zbl 1199.22001, arXiv:0807.3102).

O. Gutik, K. Pavlyk, and A. Reiter, Topological semigroups of matrix units and countably compact Brandt λ⁰-extensions, Mat. Stud. 32 (2009), no. 2, 115-131 (MR2643488 (2011b:22002), Zbl 1224.22004, arXiv:0912.0051).

O. V. Gutik, and A. R. Reiter, Symmetric inverse topological semigroups of finite rank ≤ n, Mat. Metody Fiz.-Mekh. Polya 52 (2009), no. 3, 7-14; reprinted version: J. Math. Sci. 171 (2010), no. 4, 425-432 (doi: 10.1007/s10958-010-0147-z, MR2676357 (2011e:22002), Zbl 1212.22003, arXiv:0912.0198).

O. V. Gutik, and K. P. Pavlyk, Bruck-Reilly extension of a semitopological semigroups, Applied Problems of Mech. and Math. 7 (2009), 66-72.

2010:

O. Gutik, and D. Repovš, On Brandt λ⁰-extensions of monoids with zero, Semigroup Forum 80 (2010), no. 1, 8-32 (doi: 10.1007/s00233-009-9191-8, MR2580607 (2011g:22007), Zbl 1201.20057, arXiv:0910.0535).

O. Gutik, D. Pagon, and D. Repovš, On chains in H-closed topological pospaces, Order 27 (2010), no. 1, 69-81 (doi: 10.1007/s11083-010-9140-x, MR2601156 (2011a:54037), Zbl 1221.06021, arXiv:0804.1449).

T. Berezovski, O. Gutik, and K. Pavlyk, Brandt extensions and primitive topological inverse semigroups, Int. J. Math. Math. Sci. 2010 (2010) Article ID 671401, 13 pages, (doi: 10.1155/2010/671401, MR2600883 (2011d:22002), Zbl 1225.22005, arXiv:1005.4111).

T. Banakh, S. Dimitrova, and O. Gutik, Embedding the bicyclic semigroup into countably compact topological semigroups, Topology Appl. 157 (2010), no. 18, 2803-2814 (doi: 10.1016/j.topol.2010.08.020, MR2729339 (2012a:54028), Zbl 1217.22001, arXiv:0811.4276).

I. Chuchman, and O. Gutik, Topological monoids of almost monotone, injective co-finite partial selfmaps of positive integers, Carpathian Math. Publ. 2 (2010), no. 1, 119-132 (Zbl 1404.22005, arXiv:1006.4873).

O. Gutik, and A. Reiter, On semitopological symmetric inverse semigroups of a bounded finite rank, Visn. L’viv. Univ., Ser. Mekh.-Mat. 72 (2010), 94-106 (in Ukrainian) (Zbl 1240.22003).

2011:

O. V. Gutik, K. P. Pavlyk, and A. R. Reiter, On topological Brandt semigroups, Mat. Metody Fiz.-Mekh. Polya 54 (2011), no. 2, 7-16 (in Ukrainian); English version in: J. Math. Sci. 184 (2012), no. 1, 1-11 (doi: 10.1007/s10958-012-0847-7, MR2893525 (2012m:22002), Zbl 1274.22003).

O. Gutik, and D. Repovš, Topological monoids of monotone injective partial selfmaps of ℕ with cofinite domain and image, Stud. Sci. Math. Hung. 48 (2011), no. 3, 342-353 (doi: 10.1556/SScMath.48.2011.3.1176, MR2883245, Zbl 1265.22002, arXiv:1108.2848).

I. Chuchman, and O. Gutik, On monoids of injective partial selfmaps almost everywhere the identity, Demonstr. Math. 44 (2011), no. 4, 699-722 (doi: 10.1515/dema-2013-0340, MR2906425 (2012k:22002), Zbl 1252.22002, arXiv:1009.1338).

O. Gutik, D. Pagon, and K. Pavlyk, Congruences on bicyclic extensions of a linearly ordered group, Acta Comment. Univ. Tartu. Math. 15 (2011), no. 2, 61-80 (doi: 10.12697/ACUTM.2011.15.10 , MR2961689, Zbl 1257.20059, arXiv:1111.2401).

I. Guran, O. Gutik, O. Ravsky, and I. Chuchman, On symmetric topological semigroups and groups, Visn. L’viv. Univ., Ser. Mekh.-Mat. 74 (2011), 61-73 (in Ukrainian) (Zbl 1249.22002).

I. Fihel, and O. Gutik, On the closure of the extended bicyclic semigroup, Carpathian Math. Publ. 3 (2011), no. 2, 131-157 (Zbl 1404.22006, arXiv:1201.0090).

O. Gutik, and I. Figel’, Embedding topological semigroups into idempotent generated topological semigroups, Visn. L’viv. Univ., Ser. Mekh.-Mat. 75 (2011), 106-114 (in Ukrainian) (Zbl 1265.22001).

2012:

T. Banakh, O. Gutik, O. Potiatynnyk, and A. Ravsky, Metrizability of Clifford topological semigroups, Semigroup Forum 84 (2012), no. 2, 301-307 (doi: 10.1007/s00233-011-9341-7, MR2898762, Zbl 1250.22002, arXiv:1105.2806).

O. Gutik, and D. Repovš, On monoids of injective partial selfmaps of integers with cofinite domains and images, Georgian Math. J. 19 (2012), no. 3, 511-532 (doi: 10.1515/gmj-2012-0022, MR2984503, Zbl 1256.22001, arXiv:1209.0587).

S. Bardyla, and O. Gutik, On ℋ-complete topological semilattices, Mat. Stud. 38 (2012), no. 2, 118-123 (MR3057997, Zbl 1309.22003, arXiv:1301.1152).

I. Fihel, O. Gutik, and K. Pavlyk, On a topological simple Warne extension of a semigroup, Acta Comment. Univ. Tartu. Math. 16 (2012), no. 2, 201-225 (MR3007298, Zbl 1295.22005, arXiv:1301.1232).

2013:

O. V. Gutik, and K. P. Pavlyk, Pseudocompact primitive topological inverse semigroups, Mat. Metody Fiz.-Mekh. Polya 56 (2013), no. 2, 7-19; reprinted version: J. Math. Sci. 203 (2014), no. 1, 1-15 (doi: 10.1007/s10958-014-2087-5, MR3155884, Zbl 1313.18002, arXiv:1306.2612).

O. Gutik, and K. Pavlyk, On pseudocompact topological Brandt λ⁰-extensions of semitopological monoids, Topol. Algebra Appl. 1 (2013), 60-79 (doi: 10.2478/taa-2013-0007, Zbl 1291.22003, arXiv:1306.1935).

2014:

O. Gutik, and I. Pozdnyakova, On monoids of monotone injective partial selfmaps of L_n×_lexℤ with cofinite domains and images, Algebra Discr. Math. 17 (2014), no. 2, 256–279 (MR3287933, Zbl 1327.22003, arXiv:1311.6175).

O. Gutik, On closures in semitopological inverse semigroups with continuous inversion, Algebra Discr. Math. 18 (2014), no. 1, 59–85 (MR3280257, Zbl 1315.22004, arXiv:1410.1344).

O. V. Gutik, and I. V. Pozdniakova, Congruences on the monoid of monotone injective partial selfmaps of L_n×_lexℤ with co-finite domains and images, Mat. Metody Fiz.-Mekh. Polya 57 (2014), no. 3, 7-15; reprinted version: J. Math. Sci. 217 (2016), no. 2, 139-148 (doi: 10.1007/s10958-016-2962-3, MR3379583, MR3532451, Zbl 1342.20058, arXiv:1407.6892).

2015:

O. Gutik, and O. Ravsky, On feebly compact inverse primitive (semi)topological semigroups, Mat. Stud. 44 (2015), no.1, 3-26 (MR3494696, Zbl 1356.22002, arXiv:1310.4313).

O. Gutik, and D. Repovš, On monoids of injective partial cofinite selfmaps, Math. Slovaca 65 (2015), no. 5, 981-992 (doi: 10.1515/ms-2015-0067, MR3433049, Zbl 1363.20058, arXiv:1512.03779).

O. V. Gutik, and O. V. Ravsky, Pseudocompactness, products and Brandt λ⁰-extensions of semitopological monoids, Mat. Metody Fiz.-Mekh. Polya 58 (2015), no. 2, 20-37; reprinted version: J. Math. Sci. 223 (2017), no. 1, 18-38 (doi: 10.1007/s10958-017-3335-2, MR3640275, Zbl 1349.22003, arXiv:1510.05096).

O. Gutik, On the dichotomy of a locally compact semitopological bicyclic monoid with adjoined zero, Visn. L’viv. Univ., Ser. Mekh.-Mat. 80 (2015), 33-41 (arXiv:1509.02148).

O. Gutik, and K. Mel’nyk, The semigroup of monotone co-finite partial homeomorphisms of the real line, Mathematical Bulletin of the Shevchenko Scientific Society 12 (2015), 24-40 (in Ukrainian) (arXiv:1904.06647, Zbl 1363.20057).

2016:

S. Bardyla, and O. Gutik, On a semitopological polycyclic monoid, Algebra Discr. Math. 21 (2016), no. 2, 163-183 (arXiv:1601.01151, MR3537444, Zbl 1359.22003).

O. Gutik, On the group of automorphisms of the Brandt λ⁰-extension of a monoid with zero, Proceedings of the 16th ITAT Conference Information Technologies – Applications and Theory (ITAT 2016), Tatranske Matliare, Slovakia, September 15-19, 2016. CEUR-WS, Bratislava, 2016, p. 237-240 (arXiv:1609.06085).

S. Bardyla, and O. Gutik, On a complete topological inverse polycyclic monoid, Carpathian Math. Publ. 8 (2016), no. 2, 183-194 (doi: 10.15330/cmp.8.2.183-194, arXiv:1603.08147, MR3599777, Zbl 1359.22002).

O. Gutik, Topological properties of Taimanov semigroups, Mathematical Bulletin of the Shevchenko Scientific Society 13 (2016), 29-34 (arXiv:1612.08677, Zbl 1374.22002).

O. Gutik, and I. Pozdniakova, On the monoid of monotone injective partial selfmaps of ℕ²_≤ with co-finite domains and images, Visn. L’viv. Univ., Ser. Mekh.-Mat. 81 (2016), 100-116 (arXiv:1602.06593).

O. Gutik, and O. Sobol, On feebly compact topologies on the semilattice exp_nλ, Mat. Stud. 46 (2016), no. 1, 29-43 (doi: 10.15330/ms.46.1.29-43, MR3649046, Zbl 1377.22003, arXiv:1606.00395).

O. Gutik, and K. Maksymyk, On semitopological interassociates of the bicyclic monoid, Visn. L’viv. Univ., Ser. Mekh.-Mat. 82 (2016), 98-108 (arXiv:1609.07768).

O. Gutik, and I. Pozdniakova, On the monoid of monotone injective partial selfmaps of ℕ²_≤ with co-finite domains and images, II, Visn. L’viv. Univ., Ser. Mekh.-Mat. 82 (2016), 109-127 (arXiv:1701.08015).

O. Gutik, and O. Sobol, On feebly compact shift-continuous topologies on the semilattice exp_nλ, Visn. L’viv. Univ., Ser. Mekh.-Mat. 82 (2016), 128-136 (arXiv:1702.06105).

O. Gutik, and K. Maksymyk, On semitopological bicyclic extensions of linearly ordered groups, Mat. Metody Fiz.-Mekh. Polya 59 (2016), no. 4, 31-43; reprinted version: J. Math. Sci. 238 (2019), no. 1, 32-45 (doi: 10.1007/s10958-019-04216-x, MR3924887, Zbl 1399.22007, arXiv:1608.00959).

2017:

S. Bardyla, O. Gutik, and A. Ravsky, H-closed quasitopological groups, Topology Appl. 217 (2017), 51-58 (doi: 10.1016/j.topol.2016.12.003, MR3591199, Zbl 1354.22002, arXiv:1506.08320).

O. Gutik, and A. Savchuk, On the semigroup ID_∞, Visn. L’viv. Univ., Ser. Mekh.-Mat. 83 (2017), 5-19 (in Ukrainian) (arXiv:1904.06644).

O. Gutik, On feebly compact semitopological symmetric inverse semigroups of a bounded finite rank, Visn. L’viv. Univ., Ser. Mekh.-Mat. 83 (2017), 42-57 (arXiv:1708.02064).

O. Gutik, and K. Maksymyk, On variants of the bicyclic extended semigroup, Visn. L’viv. Univ., Ser. Mekh.-Mat. 84 (2017), 22-37 (arXiv:1805.04995).

2018:

O. Gutik, On locally compact semitopological 0-bisimple inverse ω-semigroups, Topol. Algebra Appl. 6 (2018), 77-101 (doi: 10.1515/taa-2018-0008, MR3794938, Zbl 1421.22001, arXiv:1703.01434).

O. Gutik, and A. Savchuk, The semigroup of partial co-finite isometries of positive integers, Bukovyn. Mat. Zh. 6 (2018), no.1-2, 42-51 (in Ukrainian) (doi: 10.31861/bmj2018.01.042, Zbl 1424.22002, arXiv:1904.06638).

O. Gutik, and A. Ravsky, On old and new classes of feebly compact spaces, Visn. L’viv. Univ., Ser. Mekh.-Mat. 85 (2018), 48-59 (arXiv:1804.07454).

O. Gutik, and K. Melnyk, The semigroup of star partial homeomorphisms of a finite dimensional Euclidean space, Visn. L’viv. Univ., Ser. Mekh.-Mat. 86 (2018), 91-102 (in Ukrainian) (doi: 10.30970/vmm.2018.86.091-102, arXiv:1905.10736).

O. V. Gutik, and O. Yu. Sobol, On feebly compact semitopological semilattice exp_nλ, Mat. Metody Fiz.-Mekh. Polya 61 (2018), no. 3, 16-23; reprinted version: Journal of Mathematical Sciences 254 (2021), no. 1, 13-20 (doi: 10.1007/s10958-021-05284-8, MR4229020, Zbl 1438.20073, arXiv:1804.08239).

2019:

O. Gutik, and O. Sobol, Extensions of semigroups by symmetric inverse semigroups of a bounded finite rank, Visn. L’viv. Univ., Ser. Mekh.-Mat. 87 (2019), 5-36 (doi: 10.30970/vmm.2019.87.005-036, arXiv:1906.08329).

O. Gutik, and A. Savchuk, On inverse submonoids of the monoid of almost monotone injective co-finite partial selfmaps of positive integers, Carpathian Math. Publ. 11 (2019), no. 2, 296-310 (doi: 10.15330/cmp.11.2.296-310, MR4049629, Zbl 1474.20121, arXiv:1904.11802).

O. Gutik, and A. Savchuk, On the monoid of cofinite partial isometries of ℕⁿ with the usual metric, Proc. Int. Geom. Cent. 12 (2019), no. 3, 51-68 (doi: 10.15673/tmgc.v12i3.1553, MR4053279, Zbl 1452.20058, arXiv:1909.08823).

O. Gutik, and K. Maksymyk, On a semitopological extended bicyclic semigroup with adjoined zero, Mat. Metody Fiz.-Mekh. Polya 62 (2019), no. 4, 28-38 (arXiv:1911.05977).

O. Gutik, and O. Krokhmalna, The monoid of monotone injective partial selfmaps of the poset (ℕ³,≤) with cofinite domains and images, Visn. L’viv. Univ., Ser. Mekh.-Mat. 88 (2019), 32-50 (doi: 10.30970/vmm.2019.88.032-050, arXiv:2006.04481).

2020:

O. Gutik, and T. Mokrytskyi, The monoid of order isomorphisms between principal filters of ℕⁿ, Eur. J. Math. 6 (2020), no. 1, 14-36 (https://doi.org/10.1007/s40879-019-00328-5, MR4071454, arXiv:1802.03598).

T. Banakh, S. Bardyla, I. Guran, O. Gutik, and A. Ravsky, Positive answers for Koch’s problem in special cases, Topol. Algebra Appl. 8 (2020), no. 1, 76-87 (https://doi.org/10.1515/taa-2020-0007, Zbl 1441.22003, MR4083576, arXiv:1902.08895).

S. Bardyla, and O. Gutik, On the lattice of weak topologies on the bicyclic monoid with adjoined zero, Algebra Discr. Math. 30 (2020), no. 1, 26–43 (http://dx.doi.org/10.12958/adm1459, MR4195403, arXiv:1908.04566).

O. Gutik, and A. Savchuk, On the monoid of cofinite partial isometries of ℕ with the usual metric, Visn. L’viv. Univ., Ser. Mekh.-Mat. 89 (2020) 17-30 (doi: 10.30970/vmm.2020.89.017-030, Zbl 1474.20127, arXiv:2008.03159).

O. Gutik, and M. Mykhalenych, On some generalization of the bicyclic monoid, Visn. L’viv. Univ., Ser. Mekh.-Mat. 90 (2020), 5-19 (doi: 10.30970/vmm.2020.90.005-019, arXiv:2107.14118) (in Ukrainian).

O. Gutik, and P. Khylynskyi, Polycyclic extensions of semigroups, Visn. L’viv. Univ., Ser. Mekh.-Mat. 90 (2020), 20-47 (doi: 10.30970/vmm.2020.90.020-047, arXiv:2107.14408) (in Ukrainian).

2021:

T. Banakh, S. Bardyla, and O. Gutik, The Lawson number of a semitopological semilattice, Semigroup Forum 103 (2021), no. 1, 24–37 (https://doi.org/10.1007/s00233-021-10184-z, MR4276603, arXiv:1910.00436).

O. Gutik, and P. Khylynskyi, On the monoid of cofinite partial isometries of ℕ with a bounded finite noise, Proceedings of the Contemporary Mathematics in Kielce 2020, ed. Szymon Walczak. Jan Kochanowski University in Kielce, Poland. February 24-27, 2021. Sciendo, De Gruyter Poland Sp. z o.o. Warsaw, Poland, 2021, P. 127-144 (https://doi.org/10.2478/9788366675360-010, arXiv:2104.14149).

O. V. Gutik, and I. V. Pozdniakova, On the semigroup generating by extended bicyclic semigroup and an ω-closed family, Mat. Metody Fiz.-Mekh. Polya 64 (2021), no. 1, 21-34 (arXiv:2107.14075) (in Ukrainian).

O. Gutik, and M. Mykhalenych, On group congruences on the semigroup Ɓ_ω^ℱ and its homomorphic retracts in the case when a family ℱ consists of inductive non-empty subsets of ω, Visn. L’viv. Univ., Ser. Mekh.-Mat. 91 (2021), 5-27 (arXiv:2108.09543) (in Ukrainian).

O. Gutik, A note on feebly compact semitopological symmetric inverse semigroups of a bounded finite rank, Visn. L’viv. Univ., Ser. Mekh.-Mat. 91 (2021), 40-53 (arXiv:2202.08308).

Papers in Press or in Preparation

O. Gutik, and O. Lysetska, On the semigroup Ɓ_ω^ℱ which is generated by the family ℱ of atomic subsets of ω, Visn. L’viv. Univ., Ser. Mekh.-Mat. (accepted) (arXiv:2108.11354).

O. Gutik, and P. Khylynskyi, On a locally compact submonoid of the monoid cofinite partial isometries of ℕ with adjoined zero, Preprint (arXiv:2112.15000).

O. Gutik, O. Prokhorenkova, and D. Sekh, On endomorphisms of the bicyclic semigroup and the extended bicyclic semigroup, Visn. L’viv. Univ., Ser. Mekh.-Mat. (accepted) (arXiv:2202.00073) (in Ukrainian).

O. Gutik, and M. Mykhalenych, On a semitopological semigroup Ɓ_ω^ℱ when a family ℱ consists of inductive non-empty subsets of ω, Preprint (in Ukrainian, in preparation).

O. Gutik, and I. Pozdniakova, On the group of automorphisms of the semigroup Ɓ_ℤ^ℱ with the family ℱ of inductive nonempty subsets of ω, Preprint (arXiv:2206.12819).

O. Gutik, and O. Popadiuk, On the semigroup Ɓ_ω^ℱ_n which is generated by the family ℱ_n of finite bounded intervals of ω, Preprint (arXiv:2208.09155).

O. Gutik, and O. Popadiuk, On the semigroup of injective endomorphisms of the semigroup Ɓ_ω^ℱ_n which is generated by the family ℱ_n of finite bounded intervals of ω, Preprint (in preparation).

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