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Selected List of Publications

Books, Textbooks, Articles.

 

Books:

  1. Protasov I., Zarichnyi M. General Asymptology Mathematical Studies Monograph Series, 12. VNTL Publishers, Lviv, 2007. 220 pp. ISBN: 966-8849-32-9 image
  2. Teleiko, A.; Zarichnyi, M. Categorical topology of compact Hausdorff spaces. Mathematical Studies Monograph Series, 5. VNTL Publishers, Lviv, 1999. 256 pp. ISBN: 966-7148-67-X image
  3. Banakh, T.; Radul,T.; Zarichnyi, M. Absorbing sets in infinite-dimensional manifolds,VNTL, Lviv, 1996. ISBN: 5-7773-0061-8 image
  4. Zarichnyi, M. Topology of functors and monads in the category of compacta, Inst.System Stud. Education, Kyiv, 1993.
 

Textbooks:

  1. Zarichnyi, M. Elements of theory of social choice Lviv, 2001. 160 p. image
  2. Bazylevych, L.; Zarichnyi, M. Introduction to topology of infinite-dimensionalmanifolds, Kyiv, 1996.
  3. Bokalo, B.; Guran, I.; Zarichnyi, M. Book of problems of differential geometry and topology,(General topology) Inst. SystemStud. Education, Kyiv, 1994.
  4. Philosophical questions in education, Lecture Notes, Lviv University,1993 (coauthor).
  5. Guran,I.; Zarichnyi, M. Elements of theory of topological groups, Inst. SystemStud. Education, Kyiv, 1992.
  6. Guran,I.; Zarichnyi, M. Differential geometry and topology, Inst. SystemStud. Education, Kyiv, 1991.
 

Articles:

    2011:

  1. A. Savchenko, M. Zarichnyi, Probability measure monad on the category of fuzzy ultrametric spaces, Azerbaijan Journal of Mathematics, V. 1, No 1, 2011, 114–121.
  2. O. Nykyforchyn, M. Zarichnyi, Open mapping theorems for capacities, Fund. Math. 211 (2011), 1-13.

    3. 2010:

  3. L. Bazylevych, D. Repovs, M. Zarichnyi, Spaces of idempotent measures of compact metric spaces, Topol. Appl., 157 (2010), 136–144.
  4. Ì. Ì. Çàðè÷íûé, Ïðîñòðàíñòâà è îòîáðàæåíèÿ èäåìïîòåíòíûõ ìåð, Èçâ. ÐÀÍ. Ñåð. ìàòåì., 74:3 (2010), 45—64.
  5. D. Repov?s, M. Zarichnyi, On asymptotic extension dimension, Óêðà¿íñüêèé ìàòåìàòè÷íèé æóðíàë. - 2010. - N 11. - Ñ. 1523-1530.

    6. 2009:

  6. M. Zarichnyi, Coarse structure and fuzzy metrics, Matem. studii. V. 32(2009), 180–184.
  7. T. Banakh, O. Shabat, M. Zarichnyi, A universal model in?nite-dimensional space, Topology, 2009, Volume 48, Issues 2-4, Pages 186–196.
  8. Aleksandr Savchenko, Mykhailo Zarichnyi, Fuzzy ultrametrics on the set of probability measures, Topology, 2009, Volume 48, Issues 2-4, Pages 130-136.
  9. Ì. Çàði÷íèé, Á. Ïòàøíèê, Âèäàòíèé óêðà¿íñüêèé ìàòåìàòèê i ïåäàãîã Ìèðîí Çàðèöêèé (äî 120-ði÷÷ÿ âiä íàðîäæåííÿ), Âiñíèê Ëüâiâñüêîãî óíiâåðñèòåòó. Ñåð. ìåõ.-ìàò. -2009. - Âèï. 70. - Ñ. 191–207.

    10. 2008:

  10. Hubal, O., Zarichnyi, M. Probability measure monad on the category of ultrametric spaces. Appl. Gen. Topol. 9 (2008), no. 2, 229-237.
  11. Hubal, O., Zarichnyi, M. Idempotent probability measures on ultrametric spaces. J. Math. Anal. Appl. 343 (2008), no. 2, 1052--1060.
  12. Bazylevych, L., Repovs, D., Zarichnyi, M. Hyperspace of convex compacta of nonmetrizable compact convex subspaces of locally convex spaces.Topology Appl.155 (2008), no. 8, 764--772.
  13. Zarichnyi, M., Nykyforchyn, O. Capacity functor in the category of compacta. (Russian) Mat. Sb.199 (2008), no. 2, 3-26; transl. in Sb. Math. 199 (2008), no. 1-2, 159--184.
  14. Kozhan, R., Zarichnyi, M. Nash equilibria for games in capacities.Econom. Theory 35 (2008), no. 2, 321--331.
  15. O. Shukel’, M. Zarichnyi, Asymptotic dimension and symmetric powers, Math. bulletin, 2008, V. 5, 304–311.
  16. O. Shabat, M. Zarichnyi, Manifolds modeled on countable direct limits of absolute extensors , Travaux mathematiques, Press of University of Luxemburg, 2008, V. XVIII, P. 111-123.

    17. 2007:

  17. Zarichnyi, M. Spaces of measures related to dequantization. (Ukrainian) J. Phys. Stud. 11 (2007), no. 1, 34–40.
  18. Banakh, T., Zarichnyi, M. Robert Cauty: a brief biographical sketch. (Ukrainian) Mat. Stud. 27 (2007), no. 1, 105–112.
  19. Chatyrko, V.; Zarichnyi, M. A remark on asymptotic dimension and digital dimension of finite metric spaces. Mat. Stud. 27 (2007), no. 1, 100–104.
  20. Mykhailo Zarichnyi, Michael selection theorem for max-plus compact convex sets, Topology Proceedings 31 No. 2 (2007), pp. 677-681
  21. T. Banakh, B. Bokalo, I. Guran, T. Radul, M. Zarichnyi Problems from the Lviv topological seminar. In: Open Problems in Topology II, Elsevier, 2007, 655-667.
  22. T. Banakh, R. Cauty, M. Zarichnyi Open problems in in?nite-dimensional topology. In: Open Problems in Topology II, Elsevier, 2007, 601-624.

    23. 2006:

  23. Repovs, Dusan; Zarichnyi, Michael Topology of manifolds modeled on countable direct limits of Menger compacta. Topology Appl. 153 (2006), no. 17, 3230–3240.
  24. Bazylevych, L. E.; Zarichnyi, M. M. On convex bodies of constant width. Topology Appl.153 (2006), no. 11, 1699–1704.
  25. Dusan Repovs and Michael Zarichnyi, Topology of manifolds modeled on countable direct limits of Menger compacta, Topology and its Applications, Volume 153, Issue 17, 1 November 2006, Pages 3230-3240
  26. V. Frider, M. Zarichnyi, Modi?ed probability measure functor in the coarse category, Visn. nats. univ. “Lviv polytechnica”. Phys.-math. sci. 2006, N 566, 5–11.

    27. 2005:

  27. Bazylevych, L. E.; Zarichnyi, M. Hyperspaces of Radon curves and strictly convex Radon curves. Rev. Roumaine Math. Pures Appl. 50 (2005), no. 5–6, 437–442.
  28. Tymchatyn, E. D.; Zarichnyi, M. A note on operators extending partial ultrametrics. Comment. Math. Univ. Carolin. 46 (2005), no. 3, 515–524.

    29. 2004:

  29. Zarichnyi, Mykhajlo M. Space of probability measures and absolute extensors in the asymptotic category. Functional analysis and its applications, 311–316, North-Holland Math. Stud., 197, Elsevier, Amsterdam, 2004.
  30. Dranishnikov, A.; Zarichnyi, M. Universal spaces for asymptotic dimension. Topology Appl. 140 (2004), no. 2–3, 203–225.
  31. Shabat, O. Ye.; Zarichnyi, M. M. Universal maps of K\sb \omega-spaces. Mat. Stud. 21 (2004), no. 1, 71–80.
  32. Frider, V. L.; Zarichnyi, M. M. On coarse anti-Lawson semilattices. Mat. Stud. 21 (2004), no. 1, 3–12.
  33. Tymchatyn, E. D.; Zarichnyi, M. On simultaneous linear extensions of partial (pseudo)metrics. Proc. Amer. Math. Soc. 132 (2004), no. 9, 2799–2807 (electronic).

    34. 2003:

  34. Chigogidze, Alex; Zarichnyi, M. M. Universal Noebeling spaces and pseudo-boundaries of Euclidean spaces. Mat. Stud. 19 (2003), no. 2, 193–200.
  35. Skaskiv, O. B.; Vynnytskyi, B. V.; Zabolotskyi, M. V.; Zarichnyi, M. M. Myroslav Sheremeta (an attempt of scientific biography). Mat. Stud. 19 (2003), no. 1, 2–20.
  36. Guran, I.; Zarichnyi, M. Universal countable-dimensional topological groups. Proceedings of the Lviv Topological Seminar (1999/2000). Topology Appl. 128 (2003), no. 1, 55–61.
  37. Zarichnyj M. Asymptotic category and spaces of probability measures. Visn. L’viv. Univ., Ser. Mekh.-Mat. 61(2003), 211-217.
  38. Frider V., Zarichnyj M. Hyperspace functor in the coarse category. Visn. L’viv. Univ., Ser. Mekh. - Mat. 61 (2003), 78-86.

    39. 2002:

  39. Pyrch, N. M.; Zarichnyi, M. M. On a generalization of Okunev's construction. Third International Algebraic Conference in the Ukraine (Ukrainian), 346–350, National. Akad. Nauk Ukraïni, Inst. Mat., Kiev, 2002.
  40. Tymchatyn, E. D.; Zarichnyi, M. M. A note on a question of Nagata. Mat. Stud. 18 (2002), no. 2, 177–178.

    41. 2001:

  41. Chigogidze, A.; Karasev, A.; Zarichnyi, M. Topological semigroups and universal spaces related to extension dimension. Mat. Stud. 16 (2001), no. 2, 195–198.
  42. Levytska, V.; Zarichnyi, M. Spaces of nonexpanding maps: categorical properties. Mat. Stud. 16 (2001), no. 1, 3–12.
  43. Zarichny, M. M.; Ivanov, S. O. Hyperspaces of convex compact subsets of the Tikhonov cube. (Ukrainian) Ukraïn. Mat. Zh. 53 (2001), no. 5, 698–701; translation in Ukrainian Math. J. 53 (2001), no. 5, 809–813.

    44. 2000:

  44. Zarichnyi, Michael Extension property and ANR-systems. 15th Anniversary of the Chair of General Topology and Geometry at Moscow State University. Topology Appl. 107 (2000), no. 1–2, 207–214.
  45. Bazilevich, L. E.; Zarichnyi M. M.; Oleksiv, I. Ya.; Pritula, Ya. G. Ivan Mikolayovich Pesin (on the seventieth anniversary of his birth). (Ukrainian) Mat. Stud. 13 (2000), no. 1, 100.
  46. Banakh, Taras; Zarichnyi, Michael The interval [0,1] admits no functorial embedding into a finite-dimensional or metrizable topological group. Serdica Math. J. 26 (2000), no. 1, 1–4.

    47. 1999:

  47. Zarichnyi M., Levytska V. Functorial topologization of spaces of piecewise-linear maps, Appl. Mathematics. Visn. Univ. "Lviv Polytechnika 364 (1999), 216–218. (in Ukrainian)

    48. 1998:

  48. Zarichnyi, M. M. Strongly countable-dimensional resolvents of sigma-compact groups. (Russian) Fundam. Prikl. Mat. 4 (1998), no. 1, 101–108.
  49. Radul, T.; Zarichnyi, M. Nonexistence of absorbing set for a transfinite extension of covering dimension. Mat. Stud. 9 (1998), no. 1, 94–98, 111.
  50. Chigogidze A., Zarichnyi, M. On absolute extensors module a complex, Topology Appl. 86 (1998), no. 2, 169–178. 

    51. 1997:

  51. Bazylevych L., Tkach O., Zarichnyi, M. Problems on absorbing sets in hyperspacetheory and the theory of functions, MatematychniStudii, 7 (1997), no.2, 214–216.
  52. Zarichnyi, Michael Absorbing sets in the Hilbert cube related to cohomological dimension. Topology Appl. 80 (1997), no. 1–2, 195–200.
  53. Zarichnyi, M. M. Absorbing sets for n-dimensional spaces in absolutely Borel and projective classes. (Russian) Mat. Sb. 188 (1997), no. 3, 113–126; translation in Sb. Math. 188 (1997), no. 3, 435–447.

    54. 1996:

  54. E. Pentsak, Zarichnyi, M. On strongly universal k_\omega-spaces related totransfinite inductive and cohomological dimension, Methods Func. Anal.Topol., 2 (1996), no. 3–4, 122–127.
  55. M. Zarichnyi, Absorbing sets for n-dimensional spaces in absoluteborelian and projective classes, Matem. Sbornik, 188 (1996),113–126.
  56. Zarichnyi, M. Multiplication in superextensions and partial products, in: Algebraand Topology, Lviv University, (1996), 79–83, (in Russian).
  57. Zarichnyi, M. Absorbing sets in the Hilbert cube related to cohomological dimension,Topology Appl., 80 (1996), 195–200.
  58. Zarichnyi, M. Regular linear operators extending metrics: a short proof, Bull. Polish Acad. Sci. Math., 44 (1996), no. 3, 267–269.
  59. Zarichnyi, M. Universal n-soft maps of n-dimensional spaces in absolute Borelianand projective classes, Mat. zametki, 60 (1996), no. 6, 845–850. translation in Math. Notes 60 (1996), no. 5–6, 638–641 (1997).
  60. Zarichnyi, M.M., Teleiko A.B. Semigroups and monads. Algebra and topology, Lviv. Univ. Press, 1996, 84–93.

    61. 1995:

  61. Zarichnyi, Michael Some problems related to universality of maps in infinite-dimensional topology. Mat. Stud. 4 (1995), 111–114.
  62. Zarichnyi, Michael Universal map of \sigma onto \Sigma and absorbing sets in the classes of absolute Borelian and projective finite-dimensional spaces. Topology Appl. 67 (1995), no. 3, 221–230.
  63. T.N. Radul, Zarichnyi, M. Monads in the category of compacta, Uspekhi mat.nauk, 50 (1995), no. 3(303), 83–108; translation in Russian Math. Surveys 50 (1995), no. 3, 549–574.
  64. Zarichnyi, M. Universal maps and absorbing sets for countable-dimensional spaces,Matematychni Studii, 4 (1995), 85–94.

    65. 1994:

  65. L. Bazylevych, Zarichnyi M. M. On some pseudointeriors in the hyperspace of the Hilbert cube, Visn. L’viv. univ. Ser. mekh.-mat. 1994. N 38. Ñ. 26–28.

    66. 1993:

  66. Bazilevich, L. E.; Zarichnyi, M. M. On an example in the theory of soft mappings. (Ukrainian) Visnik Lviv. Univ. Ser. Mekh. Mat. No. 38 (1993), 39–41.
  67. Zarichnyi, M. On universal maps and spaces of probability measures with finite supports, Mathematical investigations (Ukrainian), Pr. Lviv. Mat. Tov.,2, Lviv. Mat. Tov., Lviv, 1993. (1993), 78–82.

    68. 1992:

  68. Zarichnyi, M. On some categorical properties of probability measures. Mathematics (Latvian), 81–88, Latv. Univ. Zinat. Raksti, 576, Latv. Univ., Riga, 1992.
  69. Zarichnyi, M. M. Some homotopy properties of functors with finite carriers. (Ukrainian) Ukraïn. Mat. Zh. 44 (1992), no. 11, 1618–1620; translation in Ukrainian Math. J. 44 (1992), no. 11, 1491–1493 (1993).
  70. Zarichnyi, M. M. Characterization of functors of G-symmetric degree and extensions of functors to the Kleisli categories. (Russian) Mat. Zametki 52 (1992), no. 5, 42–48, 141; translation in Math. Notes 52 (1992), no. 5–6, 1107–1111 (1993).
  71. Zarichnyi, M. M. Characterization of noncompact AE(n)-spaces. (Ukrainian) Ukraïn. Mat. Zh. 44 (1992), no. 7, 986–988; translation in Ukrainian Math. J. 44 (1992), no. 7, 891–892 (1993).
  72. Zarichnyi, M. M. Open normal functors with countable kernels. Application of topology in algebra and differential geometry (Tartu, 1991). Tartu Ül. Toimetised No. 940 (1992), 91–94.
  73. O. Pikhurko, Zarichnyi, M. On lifting of functors to the Eilenberg-Moore category of the triple generated by the functor C_pC_p, Ukr. mat. zh., 44(1992), no. 9, 1289–1291; translation in Ukrainian Math. J. 44 (1992), no. 9, 1181–1183 (1993).
  74. Zarichnyi, M. Absolute extensors and geometry of monad multiplication in the categoryof compacta, Matem. Sbornik, 182 (1992), 1261–1280.

    75. 1991:

  75. Zarichnyi, M. M. Continuation of natural transformations on the Kleisli category. (Ukrainian) Visnik Lviv. Univ. Ser. Mekh. Mat. No. 36 (1991), 45–49.
  76. Zarichnyi, M. M. Functors with finite supports, and n-shapes. (Ukrainian) Mathematical investigations (Ukrainian), 67–73, 118–119, Zb. Nauk. Prats Lviv. Mat. Tov., 1, Lviv. Mat. Tov., Lviv, 1991.
  77. Zarichnyi, M. Functors generated by universal mappings of injective limits of sequences of Menger compacta. (Russian) Mathematics (Russian), 95–102, Latv. Univ. Zinat. Raksti, 562, Latv. Univ., Riga, 1991.
  78. Guran, I.; Zarichnyi, M. M. The space of continuous functions, and box products. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 1991, , no. 11, 22–24 (1992); translation in Soviet Math. (Iz. VUZ) 35 (1991), no. 11, 22–24.
  79. Goldberg, A. A.; Zarichnyi, M. M.; Ptashnik, B. I. On the history of Ukrainian mathematical culture in Galicia. (Russian) Ocherki Istor. Estestvoznan. Tekhn. No. 40 (1991), 8–13.
  80. Zarichnyi, M. M. Absolute extensors and the geometry of the multiplication map of monads in the category of compacta. (Russian) Mat. Sb. 182 (1991), no. 9, 1261–1280; translation in Math. USSR-Sb. 74 (1993), no. 1, 9–27.
  81. Zarichnyi, M. M. On covariant topological functors. II. Questions Answers Gen. Topology 9 (1991), no. 1, 1–32.
  82. Zarichnyi, M. Preservation of some shape properties by functors in the category ofcompacta, Bull. Polish Acad. Sci. Math. 39, (1991), no.3–4, 235–239.
  83. Zarichnyi, M. Distributivity law for normal triples in the category of compacta andlifting of functors fo the categories of algebras, Comment. Math. Univ.Carol., 32 (1991), no.4, 785–790.

    84. 1990:

  84. Zarichnyi, M. M.; Tkach, O. I. On a topology for the space of foliations on a smooth manifold. (Ukrainian) Visnik Lviv. Univ. Ser. Mekh. Mat. No. 34 (1990), 73–75.
  85. Zarichnyi, M. M. Profinite multiplicativity of functors and a characterization of projective monads in the category of compacta. (Russian) Ukrain. Mat. Zh. 42 (1990), no. 9, 1271–1275; translation in Ukrainian Math. J. 42 (1990), no. 9, 1131–1134 (1991).
  86. Zarichnyi, M. M. On covariant topological functors. I. Questions Answers Gen. Topology 8 (1990), no. 2, 317–369.
  87. Zarichnyi, M. M.; Fedorchuk, V. V. Covariant functors in categories of topological spaces. (Russian) Translated in J. Soviet Math. 53 (1991), no. 2, 147–176. Itogi Nauki i Tekhniki, Algebra. Topology. Geometry, Vol. 28 (Russian), 47–95, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1990.

    88. 1989:

  88. Zarichnyi, M. On softness of multiplications in superextensions, in: General topology.1989, Moscow, Moscow University, 70–76, (in Russian).

    89. 1988:

  89. Zarichnyi, M. M. Functors in the category of compacta that preserve homogeneity. (Ukrainian) Visnik Lviv. Derzh. Univ. Ser. Mekh.-Mat. No. 30 (1988), 30–32, 75.
  90. Zarichnyi, M. M.; Plakhta, L. P. Lifting normal functors of finite degree to the PL category. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1988, no. 9, 5–7, 86.

    91. 1987:

  91. Zarichnyi, M. M. Groups of automorphisms and factorization of normal functors. (Ukrainian) Visnik Lviv. Derzh. Univ. Ser. Mekh.-Mat. No. 28 (1987), 64–67, 104.
  92. Zarichnyi, M. M. Operators of interiority in a sheaf topos. (Russian) Topological structures and their mappings (Russian), 62–65, iii, Latv. Gos. Univ., Riga, 1987.
  93. Banakh, T. O.; Zarichnyi, M. M. Compactifications of the iterated hyperspace functor. (Russian) Izv. Vyssh. Uchebn. Zaved. Mat. 1987, no. 10, 3–6, 74.
  94. Zarichnyi, M. M. The superextension monad and its algebras. (Russian) Ukrain. Mat. Zh. 39 (1987), no. 3, 303–309, 405.
  95. Zarichnyi, M. M. The multiplicative normal functor is a power functor. (Russian) Mat. Zametki 41 (1987), no. 1, 93–100, 121.

    96. 1986:

  96. Zarichnyi, M. Iterated superextensions, in: General topology, 1986, Moscow, Moscow University, 45–59, (in Russian).
  97. Zarichnyi, M. M. A category of normal functors. (Ukrainian) Visnik Lviv. Derzh. Univ. Ser. Mekh.-Mat. No. 25 (1986), 52–56, 103.
  98. Zarichnyi, M. M. Monadic functors of finite degree. (Russian) Problems in geometry and topology (Russian), 24–30, 92, Petrozavodsk. Gos. Univ., Petrozavodsk, 1986.

    99. 1985:

  99. Zarichnyi, M. M. Symmetric products that are finite-dimensional manifolds. (Ukrainian) Visnik Lviv. Derzh. Univ. Ser. Mekh.-Mat. No. 24 (1985), 65–69, 116.
  100. Zarichnyi, M. M. A result of J. van Mill and A. Schrijver. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1985, no. 2, 6–8, 94.

    101. 1984:

  101. Zarichnyi, M. M. The fundamental group of the superextension \lambda\sb n(X). (Russian) Mappings and functors, 24–31, 141, Moskov. Gos. Univ., Moscow, 1984.
  102. Guran, I. I.; Zarichnyi, M. M. The Whitney topology and box products. (Russian) Dokl. Akad. Nauk Ukrain. SSR Ser. A 1984, no. 11, 5–7, 87.
  103. Zarichnyi, M. M. Infinite-dimensional manifolds which arise from the direct limits of ANRs. (Russian) Uspekhi Mat. Nauk 39 (1984), no. 2(236), 153–154.

    104. 1983:

  104. Zarichnyi, M. M. Hypersymmetric powers of supercompacta. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1983, no. 1, 18–21, 100.
  105. Zarichnyi, M. Preservation of ANR(\Cal M)-spaces and infinite-dimensional manifoldsby some covariant functors, DAN SSSR, 271 (1983), 524–528.

    106. 1982:

  106. Zarichnyi, M. Free topological groups of absolute neighborhood retracts and infinite-dimensionalmanifolds, DAN SSSR, 266 (1982), 541–544.
  107. Zarichnyi, M. M. The functor \lambda \sb{n} and absolute retracts. (Russian) Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1982, no. 4, 15–19, 84.
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