About us > Staff/People > Department of Geometry and Topology

Taras Radul

Position: Professor, Geometry and Topology Department

Scientific degree: Doctor of Physical and Mathematical Sciences

Academic status: Professor

Research interests

Infinite-dimensional topology, dimension theory, theory of measure, theory of categories, asymptotic topology, theory of convex structures, game theory

Courses

Publications

Monographies:

  1. T.Banakh, T.Radul, M.Zarichnyi, Absorbing sets in infinite-dimensional manifolds. VNTL, Lviv. 1996. 232 p.
  2. T.Banakh, T.Radul. Digital topology. Text book. Lviv University Press. Lviv. 1999. 20p.
  3. R. Ardan, T.Banakh, T.Radul. Deterministic fractals. Text book. Lviv University Press. Lviv. 1997. 20p.
  4. R. Ardan, T.Banakh, T.Radul. Dynamic system and fractals. Text book. Lviv University Press. Lviv. 1997. 20p.

Articles:

  1. T.Radul. Absolute retracts and equiconnected monads.// Topology Appl. (accepted).
  2. T.Radul. Absolute extensors and binary monads // Applied Categorical Structures. (accepted)
  3. T.Banakh, T.Radul. F-Dugundji spaces, F-Milutin spaces and absolute F-valued retracts// Topology Appl. 2015, v.179, 34-50.
  4. L.Karchevska, I.Peregnyak and T. Radul . There is no monad based on Hartman-Mycielski functor // Proceedings of the Indian Academy of Sciences. Mathematical Sciences. 2014. v. 124, N1, 121 – 126.
  5. L. Karchevska, T. Radul. On extension of functors// Comment.Math.Univ.Carolin. 2012. v.53, N2, 269-279.
  6. T.Radul, V.Shomodi. An involution map for the functional monad// Mat. Stud. 2012. v. 37, N1, 29-33.
  7. L. Karchevska, T. Radul. Trivial I-fibration of the multiplication maps for monads O, OH and OS// Mat. Stud. 2012. v. 37, N2, 193-202
  8. I. Peregniak, T. Radul. A functional representation of superextension monad and linked system monad// Mat. Stud. 2012. v. 37, N2, 142-146.
  9. T.Radul. On the space of B-convex compacta// Topology Appl. 2012, v.159, 664-668.
  10. T.Radul. Convexities generated by L-monads// Applied Categorical Structures.2011. v. 19, 729-739.
  11. T.Radul. On transfinite extension of asymptotic dimension.// Topology Appl. 2010. v.157. 2292-2296.
  12. T.Radul. A functional representation of capacity monad // Topology 2009. v. 48, 100-104.
  13. T.Radul. Hyperspace as intersection of inclusion hyperspaces and idempotent measures// Mat. Stud. 2009. v. 31, 207-210.
  14. T.Radul, O.Shukel’. Functors of finite degree and asymptotic dimension// Mat. Stud. 2009. v. 31, 204-206.
  15. L. Karchevska,T.Radul. Some properties of the functor of non-expanding functionals// Mat. Stud. 2009. v. 31, 135-141.
  16. T.Radul. Convexities generated by monads (in Ukrainian) // Dopov. Ukr. Acad.of Scien. (2008). No.9. P..
  17. T.Radul, D.Repovs. Hartman-Mycielski functor of non-metrizable compacta // Proc. Indian Acad. Sci. Math. Sci. 118 (2008), 467-473.
  18. T.Radul. Absorbing spaces in Hartman-Mycielski construction//Mat. Stud. 29 (2008), 221–224.
  19. T.Banakh, B.Bokalo, I.Guran, T.Radul, M.Zarichnyi, Problems from the Lviv topological seminar // in: Open Problems in Topology, II (E.Pearl ed.), Elsevier, 2007, p.655-667.
  20. T.Radul. On universal spaces and absorbing sets related to a transfinite extension of covering dimension. // Topology Appl. 154:8 (2007), 1794–1798.
  21. T.Radul. On classification of sigma hereditary disconnected spaces // Matem. Studii. 26:1 (2006), 97–100.
  22. T.Radul. Addition and subspace theorems for asymptotic large inductive dimension // Colloq. Math. 106:1 (2006), 57–67.
  23. T.Radul, D.Repovs. On topological properties of the Hartman-Mycielski functor // Proc. Indian Acad. Sci. Math. Sci. 115:4 (2005), 477–482.
  24. T.Radul. Algebras of Lawson monads // Matem. Studii. 22:1 (2004), 21–26.
  25. T.Radul. A normal functor based on the Hartman-Mycielski construction // Mat.Studii. 19 (2003), 201-207.
  26. T.Radul. On connection between some transfinite dimensions // Topology and its Appl. 128 (2003), 49-53.
  27. T.Radul. A new transfinite dimension classifying sigma hereditary disconnected spaces // Reporte Interno N.91. Universidad Nacional de Colombia. 2002. 5p.
  28. T.Radul. Absorbing sets in countable powers of absolute retracts // Reporte Interno N.92. Universidad Nacional de Colombia. 2002. 6p.
  29. T.Radul. Functional representations of Lawson monads // Applied Categorical Structures. 9 (2001), 457-463.
  30. T.Radul. Categorical properties of iterated power // Revista Colombiana de matematicas. 5:1 (2001), 13-20.
  31. T.Radul. On strongly Lawson and I-Lawson monads // Boletin de Matematicas, 6:2 (1999), P.69-76.
  32. T.Banakh, T.Radul. Geometry of mappings of probability measure spaces (in Russian) // Mat. Stud. 11:1 (1999), 17-30.
  33. T.Radul. Topology of the space of ordering-preserving functionals // Bull.of the Polish Academy of sciences math. 47:1 (1999) 53-60.
  34. T.Radul, M.Zarichnyi. Nonexistence of absorbing sets for a transfinite extension of covering dimension // Mat.Stud. 9:1 (1998) 94–98.
  35. T.Radul. On the functor of order-preserving functionals // Comment.Math.Univ. of Caroline. 39:3 (1998) 609-615.
  36. T.Radul, Absorbing spaces for C-compacta // Topology and Appl. 83 (1998) 127–133.
  37. T.Banakh, T.Radul. On the topology of the space of probability measures and geometry of their mappings (in Russian) // Mat.Sbornik, 188:7 (1997) 23–46.
  38. T.Radul, On the space of compacta with dense set of points with non-single valued nearest point mapping // Arch. der Math. 69 (1997) 338–342.
  39. T.Radul, A functional representation of the hyperspace monad // Comment.Math.Univ. of Caroline. 38 (1997) 165-168.
  40. T.Banakh, T.Radul, On universality of countable powers of absolute retracts // Ukrainskij Mat. Zhurnal. 48:4 (1996) 540–542.
  41. T.Banakh, T.Radul. On barycentrically soft compacta and affine retracts of products of metrizable convex compacta // Mat.Stud. 6 (1996) 99-104.
  42. T.Radul, M.M.Zarichnyi, Monads in the category of compacta (in Russian) // Uspekhi Mat. Nauk. 50:3 (1995) 83-108.
  43. T.Radul, On baricentrically soft compacta // Fund.Math. 148 (1995) 27-33.
  44. T.Radul, The absorbing sets for countable-dimensional spaces // Mat. Stud. 4 (1995) 105-110.
  45. T.Banakh, T.Radul, On the functor of probability Radon measures (in Ukrainian) // Dopov. Ukr.Acad.of scien. (1994). No.8. P.16-21.
  46. T.Radul, On the baricentric map of probability measures (in Russian) // Vestnik Mosc. Univ. Ser1.1994.N.1.P.3-6.
  47. T.Radul, On certain represantations of the pseudointerior of the Hilbert cube in the probability measures spaces (in Russian) //Vestnik Mosc.Univ.Ser 1.1993.N.3.P.79-81.
  48. T.Radul, The Whithney maps for the space of hyperspaces of inclusion (in Russian) // Matematicheskie Zametki. 52:3 (1992) 117-122.
  49. T.Radul, On some properties the space of hyperspaces of inclusion (in Russian) // General topology. Spaces, maps and functors. Moscow University Press,Moscow, 1992. P.125-132.
  50. T.Radul, Monad of hyperspaces of inclusion and its algebras (in Russian) // Ukrainskyi mat.zhurnal. 42:6 (1990) 806-812.
  51. T.Radul, On modified functor of hyperspaces of inclusion (in Russian) // Isvestiya vuzov. Matematika. 1990.N.12. P.63-65.
  52. T.Radul, Monads generated by some normal functors in category of compacta (in Ukrainian) // Visnyk Lviv University.1990.iss.32.P.46-48.

Theses:

  1. T.Radul. Nash equilibrium for binary convexities//Proc. of International Conference on recent advances in Pure and Applied Mathematics. 6-9 November 2014, Antalya, Turkey. P.2025.
  2. T.Radul. Fixed point and Nash equilibrium for binary convexities //Proc. of 2014 International Conference on Topology and its Applications,July 3-7, 2014, Nafpaktos, Greece P.142.
  3. T.Radul. Non-linear extending and averaging operators //Proc. of Workshop on set theoretical methods in compact spaces and Banach spaces. April 17-21, 2013, Warsaw. P.13.
  4. T.Radul. Extending and averaging operators generated by functors//Proc. of Third International Conference on Topology and its Applications. September 2-7, 2012, Skopje, Republic of Macedonia. P.24.
  5. T.Radul. Binary convexities and monads //Proc. of International Conference dedicated to the 120th anniversary of Stefan Banach. September 17-21, 2012, Lviv, Ukraine. P.108.
  6. L. I. Karchevska, T. Radul, On extension of weakly normal functors in the category Comp onto Tych. Proc. of International Conference on Functional Analysis Dedicated to 90th Anniversary of V. E. Lyantse. 2010 L’viv, Ukraine, November 17. 39-40.
  7. T. Radul, Hyperspaces of B-convex compacta homeomorphic to a Hilbert cube manifold. Proc. of International Conference on Functional Analysis Dedicated to 90th Anniversary of V. E. Lyantse. 2010 L’viv, Ukraine, November 17. 59-60.
  8. T.Radul. A functional representation of capacity monad. Proc. of International Conference “Infinite Dimensional Analysis and Topology”. May 27 – June 1, 2009. Ivano-Frankivsk, Yaremche, Ukraine.
  9. T.Radul, O.Shukel’. Funktors of finite degree in the asymptotic category and asymptotic dimension. Proc. of International Conference “Infinite Dimensional Analysis and Topology”. May 27 – June 1, 2009. Ivano-Frankivsk, Yaremche, Ukraine. 125–126.
  10. T.Radul. Transfinite extension of asymptotic dimension// Intern. Conf. “Analysis and Topology. Lviv -2008”, 1-8 June, 2008, p.56-57.
  11. L. Karchevska,T.Radul. The functor of non-expanding functionals is not open// Intern. Conf. “Analysis and Topology. Lviv -2008”, 1-8 June, 2008, p.34-35.
  12. T.Radul. On asymptotic dimension. Actas LXXVII Encuentro Sociedad Matematica de Chile. 3-5 November, 2005. Olmue.Chile. P.7-8.
  13. T.Radul. Some properties of asymptotic inductive dimension. Actas XV Congreso de Matematicas Capricornio. 3-6 Agosto, 2005. Antofagasta.Chile.
  14. T.Radul. On the transfinite extension of asymptotical inductive dimension// 3rd Japan-Mexico Joint Meeting on Topology and its Applications, December 6 -10, 2004,Oaxaca, Mexico. p.56-57.
  15. T.Radul. Topological and categorical properties of Hartman-Mycielski construction// Proc. of International Conference dedicated to 125th ann. of Hahn. P.157-158.Chernivtsi, June 27- Julay 3, 2004
  16. T.Radul. Universal spaces related to some transfinite dimension// Proc. of International Conference “Geometric Topology: Infinite-dimensional Topology, Absolute Extensors, Application”.P.62-63. Lviv, May 26-30, 2004
  17. T.Radul. On Lawson monads and its algebras // IV International Algebraic Conference in Ukraine. Lviv. 2003. P.190
  18. T.Radul . On Lawson monads // Memorias de 9 Nacional Simposio de matematicas.p.56-57. Bogota, Colombia. 2000
  19. T.Radul, Absorbing spaces related to C-compacta // Borsuk & Kuratowski session. Warszawa. 1996.
  20. T.Radul, Borelian subset in the space of probability measures //Proc. IX Intern. Conf. on Top. and Appl. Kiev,1992. P.115.
  21. T.Radul, The pairs of probability measures spaces homeomorphic to (Q,S) (in Russian)// Proc. VI Simp. Tirasp. on Gen. Top. and Appl.-Chisinau, 1991.-P.176-177.
  22. T.Radul, On instrict characterisation of algebras generated by some functors in category of compacta (in Russian)// Proc.Symp.on theory of rings, algebras and moduli.Lviv. 1990.P.9-10.

Biography

Birthday: 18th of May 1965

Studied at Ivan Franko National University of Lviv in 1982-1983, 1985-1989.

Master Thesis: “Modified inclusion hyperspace functor”, defended in 1989 under supervising of M.Zarichnyi

Then studied at Lomonosov Moscow State University in 1989-1992.

Ph.D.Thesis: “Infinite-Dimensional Manifolds and Bundles in the Theory of Some Covariant Functors”, defended in 1992 in Lomonosov Moscow State University under supervision of V.V.Fedorchuk.

Thesis of Doktor of Science: “Infinite-Dimensional Spaces and Mappings in the Category Theory”, defended in 2008 in Institute of Mathematics of NASU (Kyiv, Ukraine).

Employment:

1993-1995 – Physical and Mathematical Lyceum 
1995-1996 – Ya. Pidstryhach Institute of Applied Problems of Mechanics and Mathemactics of National Academy of Sciences
1998-1999 – Visiting Professor at Dokuz Eylul University (Turkey) by NATO Science Fellowship in Mathematics
2000-2002 – Associate Professor at Universidad Nacional de Colombia
2005-2006 – Associate Professor at Universidad de Concepcion (Chile)
1996-2010 – Docent at the department of Geometry and Topology of Ivan Franko National University of Lviv
2010-present – Professor at the department of Geometry and Topology of Ivan Franko National University of Lviv

Coauthors: R.Ardan, T.Banakh, B.Bokalo, I.Guran, D.Repovs, M.Zarichnyi, L.Karchevska, I.Peregnyak, V.Shomodi

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