Категорна топологія, теорія ігор, теорія опуклості, теорія вимірів, теорія міри, нескірченно-вимірна топологія.

• Алгебра та геометрія (113 Прикладна математика)
• Топологія та диференціальна геометрія

Scientific papers

1. T.Radul. Fibration of idempotent measures. Ukr.Mat.Zhurnal. 2020. V.72, N.10, P.1544-1552.

2. T.Radul. Idempotent measures: absolute retracts and soft maps. Topological Methods in Nonlinear Analysis. 2020. V.56, P. 161-172.

3. T.Radul, On the openness of the idempotent barycenter map, Topology and its Applications. 2019. V. 265, 106809

4. T. Radul A functional representation of the capacity multiplication monad.
Visnyk of the Lviv Univ. Series Mech. Math. 2018. Issue 86. P. 125-133

5. T. Radul. Equilibrium under uncertainty with Sugeno payoff. Fuzzy Sets and sytems. 2018. v.349, p.64-70.

6. T. Radul. Equilibria for games in idempotent measures. ESAIM. Proceedings and surveys. 2017, Vol. 57, p. 64-69.

7. T.Radul. Monads and tensor products. Ukr. Mat. Zh. 2017. v.69, № 6. – p. 854-859

8. T.Radul. Absolute extensors and binary monads. Applied Categorical Structures. 2017. v. 25. p.269–278

9. T.Radul. Nash equilibrium for binary convexities // Topological Methods in Nonlinear Analysis 2016, v.48. p.555-564

10. T.Radul. Absolute retracts and equiconnected monads.// Topology Appl. 202 (2016), 1–6.

11. T.Banakh, T.Radul. F-Dugundji spaces, F-Milutin spaces and absolute F-valued retracts// Topology Appl. 2015, v.179, 34-50.

12. 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, n.1, 121-126.

13. L. Karchevska, T. Radul. On extension of functors// Comment.Math.Univ.Carolin. 2012. v.53, N2, 269-279.

14. T.Radul, V.Shomodi. An involution map for the functional monad// Mat. Stud. 2012. v. 37, N1, 29-33.

15. 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.

16. Peregniak, T. Radul. A functional representation of superextension monad and linked system monad// Mat. Stud. 2012. v. 37, N2, 142-146.

17. T.Radul. On the space of B-convex compacta// Topology Appl. 2012, v.159, 664-668.

18. T.Radul. Convexities generated by L-monads// Applied Categorical Structures. 2011. v. 19, 729-739.

19. T.Radul. On transfinite extension of asymptotic dimension.// Topology Appl. 2010. v.157. 2292–2296.

20. T.Radul. A functional representation of capacity monad // Topology 2009. v. 48, 100-104.

21. T.Radul. Hyperspace as intersection of inclusion hyperspaces and idempotent measures// Mat. Stud. 2009. v. 31, 207-210.

22. T.Radul, O.Shukel’. Functors of finite degree and asymptotic dimension// Mat. Stud. 2009. v. 31, 204-206.

23. L. Karchevska,T.Radul. Some properties of the functor of non-expanding functionals// Mat. Stud. 2009. v. 31, 135-141.

24. T.Radul. Convexities generated by monads// Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky. 2008, No. 9, 27-30.

25. T.Radul, D.Repovs. Hartman-Mycielski functor of non-metrizable compacta Proceedings of the Indian Academy of Sciences. Mathematical Sciences// 2008 v.118, 467-473..

26. T.Radul. Absorbing spaces in Hartman-Mycielski construction Mat. Stud// 2008,
v. 29,221–224.

27. T.Banakh, B.Bokalo, I.Guran, T.Radul, M.Zarichnyi. Problems from the Lviv topological seminar. In book: Open problems in topology II.Elsevier B.V. 2007. p.655-667

28. T.Radul. On universal spaces and absorbing sets related to a transfinite extension of covering dimension// Topology Appl. 2007, v.154, 1794–1798.

29. T.Radul. On classification of sigma hereditary disconnected spaces// Mat. Stud. 2006.v.26. P.97-100.

30. T.Radul. Addition and subspace theorem for asymptotic large inductive dimension.
//Colloq. Math. 2006.v. 106 , P.57-67.

31. T.Radul, D.Repovs. On topological properties of the Hartman-Mycielski functor// Proceedings of the Indian Academy of Sciences. Mathematical Sciences. 2005 v.115, N4, P.477-482.

32. T.Radul. Lawson monads and projectivity// Visn. L’viv. Univ., Ser. Mekh.-Mat. 2004, No. 63, 131-134

33. T.Radul. Algebras of Lawson monads// Mat. Stud. 2004.v.22. P.21-26

34. T.Radul. On connection between some transfinite dimensions// Topology Appl. 2003 v.128. P.49-53. 2003.

35. T.Radul. A normal functor based on the Hartman-Mycielski construction// Mat.Stud. 2003. v19. P.201-207. Zbl 1023.54017

36. T.Radul. Functional representations of Lawson monads.// Applied Categorical Structures. 2001, v9, P.457-463.

37. T.Radul. Categorical properties of iterated power.// Revista Colombiana de matematicas. 2001, v.35, N1, P.13-20.

38. T.Radul. On strongly Lawson and I-Lawson monads// Boletin de Matematicas 1999, v.6, N2, P.69-76.

39. T.Banakh, T.Radul. Geometry of mappings of probability measure spaces (in Russian),//Mat. Stud. 1999, v.11,N 1, P.17-30.

40. T.Radul. Topology of the space of ordering-preserving functionals,//Bull. Pol. Acad. Sci., Math. 1999, v.47, N 1, P.53-60.

41. T.Radul, M.Zarichnyi. Nonexistence of absorbing sets for a transfinite extension of covering dimension,// Mat.Stud. 1998, v.9 N 1, P. 94-98.

42. T.Radul. On the functor of order-preserving functionals,//Commentat. Math. Univ. Carol. 1998. v.39, N3, P.609-615.

43. T.Radul, Absorbing spaces for C-compacta// Topology Appl. 1998 v.83. P.127–133.

44. T.Banakh, T.Radul. On the topology of the space of probability measures and geometry of their mappings (in Russian),// Mat. Sbornik. 188, No.7, 23-46 (1997)

45. T.Radul, On the space of compacta with dense set of points with non-single valued nearest point mapping.// Arch. Math. 1997.v.69.P.338-342. Zbl 0916.54010

46. T.Radul, A functional representation of the hyperspace monad// Commentat. Math. Univ. Carol. 1997.v.38.P.165-168.

47. T.Banakh, T.Radul, On universality of countable powers of absolute retracts//
Ukr. Mat. Zh. 48, No.4, 540-542 (1996).

48. T.Banakh, T.Radul. On barycentrically soft compacta and affine retracts of products of metrizable convex compacta// Mat.Stud. 1996.v.6. P.99-104. Zbl 0974.46507

49. T.Radul, M.M.Zarichnyi, Monads in the category of compacta (in Russian)// Uspiekhi Mat. Nauk 50, No.3, 83-108 (1995

50. T.Radul, On barycentrically soft compacta//Fund.Math.1995.v.148. P.27-33.

51. T.Radul, The absorbing sets for countable-dimensional spaces//Mat. Stud.1995.v.4. P.105-110.

52. T.Banakh, T.Radul, On the functor of probability Radon measures (in Ukrainian)// Dopov. Ukr. Acad. Sci. 1994. issue 8. P.16-21.

53. T.Radul, On the baricentric map of probability measures (in Russian)// Vestn. Mosk. Univ., Ser. I 1994, No.1, 3-6 (1994).

54. T.Radul, On certain represantations of the pseudointerior of the Hilbert cube in the probability measures spaces (in Russian) Vestn. Mosk. Univ., Ser. I 1993, No.3, 79-81 (1993)

55. T.Radul, The Whithney maps for the space of hyperspaces of inclusion (in Russian, English) // Mat. Zametki 52, No.3, 117-122 (1992).

56. T.Radul, On some properties of the space of hyperspaces of inclusion (in Russian) // Fedorchuk,V.V. (ed.) et al., General topology. Spaces, mappings and functors. Collection of scientific works. Moskva: Izdatel’stvo Moskovskogo Universiteta. 125-132 (1992).

57. T.Radul, Monad of hyperspaces of inclusion and its algebras (in Russian) //
Ukr. Mat. Zh. 42, No.6, 806-811 (1990).

58. T.Radul, On modified functor of hyperspaces of inclusion (in Russian) //
Izv. Vyssh. Uchebn. Zaved.,Mat. No.12(34), 63-65 (1990).

59. T.Radul, Monads generated by some normal functors in category of compacta (in Ukrainian)//Trans.Lviv University.1990.iss.32.P.46-48.

Abstracts

60. T. Radul Topological properties of idempotent barycenter map. In¬ter-national Conference to the 70th anniversary of Anatolij Plichko. June 26– 29. – Lviv, Ukraine, 2019. – P. 99-100.

61. T. Radul Nash equilibrium for games with payoff expressed by fuzzy integrals // In book of Proceeding of 2019 Interdisciplinary Colloquium in Topology and its Applications June 19-22, Vigo,2019.– P. 125-126.

62. T. Radul Openness of the idempotent barycenter map // Emerging Trends in Applied Mathematics and Mechanics 2018 Krakow, June 18 – 22, 2018 . – P. 168

63. T. Radul On the idempotent barycenter map. In¬ter¬national Conference in Functional Analisis dedicated to the 125th anniversary of Stefan Banach: Abtract of Reports, September 18– 23. – Lviv, Ukraine, 2017. – P. 78

64. T. Radul. Max-Plus convex compacta: a categorical approach. International conference dedicated to the 120th anniversary of Kazimierz Kuratowski, Lviv September 27 – October 1, 2016

65. T. Radul. Equilibrium for convexities generated by monads and applications to games in capacities. ETAMM 2016 May 30 – June 3, 2016, Perpignan, France

66. 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.202

67. 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.

68. 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.

69. 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.

70. 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.

71. 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.

72. 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.

73. 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.

74. 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. .

75. L. Karchevska, T.Radul. The functor of non-expanding functionals is not open, Proc. of International Conference “Analisys and Topology”, L’viv, June 2-7, 2008, 34—35.

76. T.Radul. Transfinite extension of asymptotic dimension. Proc. of International Conference “Analisys and Topology”, L’viv, June 2-7, 2008, 56–57.

77. T.Radul. On asymptotic dimension. Actas LXXVII Encuentro Sociedad Matematica de Chile. 3-5 November, 2005. Olmue.Chile. P.7-8.

78. T.Radul. Some properties of asymptotic inductive dimension. Actas XV Congreso de Matematicas Capricornio. 3-6 Agosto, 2005. Antofagasta.Chile.

79. T.Radul. On the transfinite extension of asymptotical inductive dimension.
Proc of III Joint Meeting Japan-Mexico in Topology and its Applications.
Oaxaca, Mexico. December 6-10, 2004.

80. 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

81. 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

82. T.Radul. On Lawson monads and its algebras//Proc. of IV International Algebraic Conference in Ukraine. Lviv. 2003. P.190

83. T.Radul . On Lawson monads.// Memorias de 9 Nacional Simposio de matematicas.p.56-57. Bogota, Colombia. 2000

84. T.Radul, Absorbing spaces related to C-compacta// Borsuk & Kuratowski session. Warszawa. 1996.

85. T.Radul, Borelian subset in the space of probability measures//Proc. IX Intern. Conf. on Top. and Appl. Kiev,1992. P.115.

86. 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.

87. 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.

Books

88. T.Banakh, T.Radul, M.Zarichnyi, Absorbing sets in infinite-dimensional manifolds. VNTL, Lviv. 1996. 232 p.

Scientic reports

89. T.Radul. A new transfinite dimension classifying sigma hereditary disconnected spaces.// Reporte Interno N.91. Universidad Nacional de Colombia. 2002. 5p.

90. T.Radul. Absorbing sets in countable powers of absolute retracts// Reporte Interno N.92. Universidad Nacional de Colombia. 2002. 6p.

Text books

91. T.Banakh, T.Radul. Digital topology. Text book. Lviv University Press. Lviv. 1999. 20p.

92. R. Ardan, T.Banakh, T.Radul. Deterministic fractals. Text book. Lviv University Press. Lviv. 1997. 20p.

93. R. Ardan, T.Banakh, T.Radul. Dinamic system and fractals. Text book. Lviv University Press. Lviv. 1997. 20p.

Народився на Львівщині, в 1989 закінчив Львівський державний університет ім.І Франка.

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