Dmitri Shakhmatov

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    MONOGRAPH

  1. Algebraic structure of pseudocompact groups (with D.Dikranjan), Memoirs of the American Mathematical Society 133/633 (1998), 83 pp.

    PAPERS PUBLISHED IN REFEREED JOURNALS

  2. Cardinal invariants of topological fields (in Russian), Doklady Akademii Nauk SSSR 271 (1983), 1332-1336; English transl., Soviet Math. Doklady 28 (1) (1983), 290-294.

  3. Embeddings into topological fields and construction of a field the space of which is not normal (in Russian), Commentationes Mathematicae Univ. Carolinae 24 (1983), 525-540.

  4. On one-to-one continuous mappings of universal topological algebras which preserve continuity of operations and decrease the weight (in Russian), Vestnik Moskov. Univ. Ser I Matem. Mekh. 2 (1984), 42-45; English transl., Moscow Univ. Math. Bulletin 39 (2) (1984), 57-60.

  5. No upper bound for cardinalities of Tychonoff c.c.c. spaces with a $G_\delta$-diagonal exists. (An answer to J.Ginsburg and R.G.Woods' question.), Commentationes Mathematicae Univ. Carolinae 25 (1984), 731-746.

  6. On pseudocompact spaces with a point-countable base (in Russian), Doklady Akademii Nauk SSSR 279 (1984), 825-829; English transl., Soviet Math. Doklady 30 (3) (1984), 747-751.

  7. Character and pseudocharacter in minimal topological groups (in Russian), Matematicheskie Zametki 38 (1985), 908-914; English transl., Math. Notes 38 (5-6) (1985), 1003-1006.

  8. When is a space $C_p(X)$ $\sigma$-countably compact? (with V.V.Tkachuk) (in Russian), Vestnik Moskov. Univ. Ser. I Matem. Mekh. 1 (1986), 70-72; English transl., Moscow Univ. Math. Bulletin 41 (1986), 73-75.

  9. Continuous homomorphic images of groups with a countable base do not cover all groups with a countable network(with V.G.Pestov) (in Russian), Vestnik Moskov. Univ. Ser. I Matem. Mekh. 3 (1986), 98-101; English transl., Moscow Univ. Math. Bulletin 41 (3) (1986), 92-95.

  10. $S$- and $L$-fields (in Russian), Vestnik Moskov. Univ. Ser. I Matem. Mekh. 5 (1986), 72-73; English transl., Moscow Iniv. Math. Bulletin 41 (5) (1986), 66-68.

  11. Precalibers of $\sigma$-compact groups (in Russian), Matematicheskie Zametki 39 (1986), 859-868; English transl., Math. Notes 39 (5-6) (1986), 465-470.

  12. A pseudocompact Tychonoff space all countable subsets of which are closed and $C^*$-embedded, Topology and its Applications 22 (1986), 139-144.

  13. A regular symmetrizable $L$-space, Comptes Rendus of the Bulgarian Academy of Sciences 40 (11) (1987), 5-8.

  14. The structure of topological fields and cardinal invariants (in Russian), Trudy Moskov. Matem. Obschestva 50 (1987), 249-259; English transl., Transactions of the Moscow Math. Society (1988), 251-261.

  15. Closed embeddings into pseudocompact spaces preserving dimensions (in Russian), Vestnik Moskov. Univ. Ser I Matem. Mekh. 1 (1988), 69-71; English transl., Moscow Univ. Math. Bulletin 43 (1) (1988), 57-59.

  16. On pointwise approximation of arbitrary functions by countable families of continuous functions (with A.V.Arhangel'skii) (in Russian), Trudy seminara imeni I.G.Petrovskogo 13 (1988), 206-227; English transl., Journal of Soviet Math. 50 (1990), 1497-1512.

  17. Zerodimensionality of free topological groups and topological groups with non-coinciding dimensions, Bulletin of the Polish Academy of Sciences, ser. Math. 37 (7-12) (1989), 497-506.

  18. A problem of coincidence of dimensions in topological groups, Topology and its Applications 33 (1989), 105-113.

  19. Pseudocompact topologizations of groups (with D.Dikranjan), Zbornik radova filosofskog fakulteta u Nisu 4 (1990), 83-93.

  20. Dugundji spaces and topological groups, Commentationes Mathematicae Univ. Carolinae 31 (1990), 129-143.

  21. Products of minimal Abelian groups (with D.Dikranjan), Mathematische Zeitschrift 204 (1990), 583-603.

  22. Imbeddings into topological groups preserving dimensions, Topology and its Applications 36 (1990), 181-204.

  23. Critical power of minimality of topological groups close to being compact (with D.Dikranjan), Comptes Rendus of the Bulgarian Academy of Sciences 43 (10) (1990), 13-15.

  24. $\alpha_i$-properties in Frechet-Uryshon topological groups, Topology Proceedings 15 (1990), 143-183.

  25. Final compactness and separability in regular symmetrizable spaces (in Russian), Trudy seminara imeni I.G.Petrovskogo 15 (1991), 196-220; English transl., Journal of Soviet Math. 60 (1992), 1796-1815.

  26. Zerodimensionality of subgroups of locally compact groups, Commentationes Mathematicae Univ. Carolinae 32 (1991), 581-582.

  27. Compact-like totally dense subgroups of compact groups (with D.Dikranjan), Proceedings of the American Mathematical Society 114 (1992), 1119-1129.

  28. Cartesian products of Frechet-Urysohn topological groups and function spaces (with V.I.Malykhin), Acta Math. Hungarica 60 (3-4) (1992), 207-215.

  29. Pseudocompact topologies on groups (with D.Dikranjan), Topology Proceedings 17 (1992), 335-342.

  30. Pseudocompact and countably compact topological groups: Cartesian products and minimality (with D.Dikranjan), Transactions of the American Mathematical Society 335 (1993), 775-790.

  31. Metrizability of topological groups having weak topologies with respect to good covers (with T.Nogura and Y.Tanaka), Topology and its Applications 54 (1993), 203-212.

  32. A note on transfinite inductive dimensions in topological groups, Topology and its Applications 54 (1993), 213-220.

  33. A universal complete metric Abelian group of a given weight (with J.Pelant and S.Watson), in: Topology with Applications, Szekszard (Hungary), Bolyai Society Mathematical Studies 4 (1993), 431-439.

  34. A direct proof that every infinite compact group $G$ contains $\{0,1\}^{w(G)}$, in: Papers on General Topology and Applications (Eighth Summer Conference at Queens College), Annals of the New York Academy of Sciences 728 (1994), 276-283.

  35. Factorization of mappings of topological spaces and homomorphisms of topological groups in accordance with weight and dimension ind (in Russian), Trudy seminara imeni I.G.Petrovskogo 17 (1994), 215-243; English transl., Journal of Mathematical Sciences 75 no. 3 (1995), 1754-1769.

  36. Amalgamation of convergent sequences in locally compact groups (with T.Nogura), Comptes Rendus de l'Academie des Sciences de Paris Ser. I, 320 (1995), 1349-1354.

  37. Large families of dense pseudocompact subgroups of compact groups (with G.Itzkowitz), Fundamenta Mathematicae 147 (1995), 197-212.

  38. When does the Fell topology on a hyperspace of closed sets coincide with the meet of the upper Kuratowski and the lower Vietoris topologies? (with T.Nogura), Topology and its Applications 70 (1996), 213-243.

  39. A characterization of Dugundji spaces in terms of set-valued maps (with V.Valov), Topology and its Applications 74 (1996), 109-121.

  40. Dense countably compact subgroups of compact groups (with G.Itzkowitz), Mathematica Japonica 45, no. 3 (1997), 497-501.

  41. Characterizations of intervals via continuous selections (with T. Nogura), Rendiconti del Circolo Matematico di Palermo, Serie II, 46 (1997), 317-328.

  42. Haar nonmeasurable partitions of compact groups (with G.Itzkowitz), Tsukuba Journal of Mathematics 21, no. 1 (1997), 251-262.

  43. Spaces which have finitely many continuous selections (with T. Nogura), Bollettino dell'Unione Matematica Italiana (7), 11-A (1997), 723-729.

  44. $A$-property versus $\alpha_4$-property in topological spaces and groups (with T.Nogura and Y.Tanaka), Studia Scientiarum Mathematicarum Hungarica, 33 (1997), 351-362.

  45. Neither first countable nor Cech-complete spaces are maximal Tychonoff connected (with M.G.Tkacenko, V.V.Tkachuk, S.Watson and R.G.Wilson), Proceedings of the American Mathematical Society 126 (1998), 279-287.

  46. A categorical version of the Lefschetz-Nobeling-Pontryagin theorem on embedding compacta in R^n, Topology and its Applications 85 (1998), 345-349.

  47. A relatively free topological group that is not varietal free (with V.G.Pestov), Colloquium Mathematicum 77 (1998), 1-8.

  48. Baire isomorphisms at the first level and dimension, Topology and its Applications 107 (2000), 153-159.

  49. Topological groups with dense compactly generated subgroups (with H. Fujita), Applied General Topology 3 (2002), 85-89.

  50. A compact Hausdorff topology that is a T1 complement of itself (with M. Tkachenko), Fundamenta Mathematicae 175 (2002), 163-173.

  51. Strengthening connected Tychonoff topologies (with M.Tkachenko, V.Tkachuk, R. Wilson), Applied General Topology 3 (2002), 113-131.

  52. A characterization of compactly generated metric groups (with H.Fujita), Proceedings of the American Mathematical Society 131 (2003), 953-961.

  53. Transversal and T1-independent topologies (with M. Tkachenko and R. Wilson), Houston Journal of Mathematics, 30 (2004), 421-433.

  54. Examples concerning extensions of continuous functions (with C.Costantini), Topology and its Applications, 143 (2004), 189-208.

  55. Forcing hereditarily separable compact-like group topologies on Abelian groups (with D. Dikranjan), Topology and its Applications, 151 (2005), 2-54.

  56. Weight of closed subsets topologically generating a compact group (with D. Dikranjan), Mathematische Nachrichten, 280 (2007), no. 5-6, 505-522.

  57. Reflection principle characterizing groups in which unconditionally closed sets are algebraic (with D. Dikranjan), Journal of Group Theory, 11 (2008), no. 3, 421-442 (earlier version is available as ArXiv preprint math.GR/0703304).

  58. Building suitable sets for locally compact groups by means of continuous selections, Topology and its Applications, 156 (2009), 1216-1223 (available as ArXiv preprint arXiv:0812.0489).

  59. Minimal pseudocompact group topologies on free abelian groups (with D. Dikranjan and A. Giordano Bruno), Topology and its Applications, 156 (2009), 2039-2053 (available as ArXiv preprint arXiv:0811.0914).

  60. Quasi-convex density and determining subgroups of compact abelian groups (with D. Dikranjan), Journal of Mathematical Analysis and Applications 363 (2010), 42-28 (extended version available as ArXiv preprint arXiv:0807.3846).

  61. Group-valued continuous functions with the topology of pointwise convergence (with J. Spevak), Topology and its Applications, 157 (2010), 1518-1540 (available as ArXiv preprint arXiv:0907.4941).

  62. Hewitt-Marczewski-Pondiczery type theorem for abelian groups and Markov's potential density (with D. Dikranjan), Proceedings of the American Mathematical Society, 138 (2010), 2979-2990 (available as ArXiv preprint arXiv:0912.0497).

  63. The Markov-Zariski topology of an abelian group (with D. Dikranjan), Journal of Algebra, 324 (2010), 1125-1158 (available as ArXiv preprint arXiv:1005.1149).

  64. Productivity of sequences with respect to a given weight function (with D. Dikranjan and J. Spevak), Topology and its Applications, 158 (2011), 298-324 (available as ArXiv preprint arXiv:1011.1524).

    SURVEY PAPERS

  65. A survey of current researches and open problems in the dimension theory of topological groups, Questions and Answers in General Topology 8 (1) (1990), 101-128.

  66. Compact spaces and their generalizations, pp. 522-589 in: Recent Progress in General Topology (M.Husek and Jan van Mill, Eds.) (North-Holland, Amsterdam, 1992).

  67. A selective survey of results and open problems concerning topological groups, fields and vector spaces, Topology and its Applications, 91 (1999), 51-63.

  68. Convergence in the presence of algebraic structure, pp. 463-484 in: Recent Progress in General Topology, II (M.Husek and Jan van Mill, Eds.) (North-Holland, Amsterdam, 2002).

  69. Topological rings, division rings, fields and lattices, pp. 365-371 in: Encyclopedia of General Topology (K.P. Hart, J. Nagata, J.E. Vaughan, Eds.) (North-Holland, Amsterdam, 2004).

  70. Consonant (splittable) spaces, pp. 53-55 in: Encyclopedia of General Topology (K.P. Hart, J. Nagata, J.E. Vaughan, Eds.) (North-Holland, Amsterdam, 2004).

  71. Selected topics from the structure theory of topological groups (with D. Dikranjan), pp. 389-406 in: Open Problems in Topology II (E. Pearl, Eds.) (North-Holland, Amsterdam, 2007).

    PAPERS ACCEPTED FOR PUBLICATION IN REFEREED JOURNALS

  72. Convergent sequences in minimal groups, to appear in: Topology and its Applications (available as ArXiv preprint arXiv:0901.0175).

  73. Quasi-convexly dense and suitable sets in the arc component of a compact group (with D. Dikranjan), to appear in: Mathematische Nachrichten.

  74. A Kronecker-Weyl theorem for subsets of abelian groups (with D. Dikranjan), to appear in: Advances in Mathamatics (available as ArXiv preprint arXiv:1012.4177).

    OTHER PUBLICATIONS

  75. The Baire property and linear isomorphisms of spaces of continuous functions (with O.G.Okunev) (in Russian), pp. 89-92 in: Topological structures and their mappings (Latv. Gosud. Univ., 1987); English Abstract in: MR 89g: 54067.

  76. Minimal topologizations of free groups (in Russian), pp. 97-100 in: Algebra, Logic and Theory of Numbers (O.B.Lupanov and A.I.Kostrikin, Eds.) (Izd-vo Moskov. Univ., Moscow, 1986).

  77. Two topics on topological groups, pp. 102-108 in: Conference/Workshop on General Topology and Geometric Topology (University of Tsukuba, June 1991).

  78. A strong counterexample to the classical Dirichlet problem in potential theory (with S.Watson), pp. 163-168 in: Proceedings of Joint Conference on Applied Mathematics (Research Institute of Mathematical Sciences of Kyoto University, December 20-22, 1993).

  79. Some open problems concerning topological groups, fields and vector spaces, pp. 75-86 in: Proceedings of General Topology Symposium (Saitama University, December 6-8, 1993).

  80. Electronic access for topology resources (with B.Brechner, M.Mislove, and S.Watson), in: Papers on General Topology and Applications (Tenth Summer Conference at Amsterdam), Annals of the New York Academy of Sciences 788 (1996), 1-8.
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