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 Uspekhi Mat. Nauk, 1980, Volume 35, Issue 3(213), Pages 3–22 (Mi umn3355)

International Topology Conference
Survey lectures

Relations among the invariants of topological groups and their subspaces

A. V. Arkhangel'skii

Abstract: In this paper we study topological properties of topological groups and, first of all, cardinal invariants of topological groups. Many of the relevant questions are subsumed under the following general scheme: how does the compatibility of the topology with the group structure reflect on the relations among the invariants of this topology?
We use the notation and terminology of $\lbrack 4\rbrack$. Cardinal invariants of a topological group are understood to mean those of its underlying space, which is assumed throughout to be completely regular and $T_1$. Proofs are given in condensed form or omitted altogether.

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English version:
Russian Mathematical Surveys, 1980, 35:3, 1–23

Bibliographic databases:

MSC: 22A05, 54B05, 54A25, 22A25

Citation: A. V. Arkhangel'skii, “Relations among the invariants of topological groups and their subspaces”, Uspekhi Mat. Nauk, 35:3(213) (1980), 3–22; Russian Math. Surveys, 35:3 (1980), 1–23

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. V. Arkhangel'skii, “Classes of topological groups”, Russian Math. Surveys, 36:3 (1981), 151–174
2. V. V. Tkachuk, “On a method of constructing examples of $M$-equivalent spaces”, Russian Math. Surveys, 38:6 (1983), 135–136
3. V. G. Pestov, “Some topological properties preserved by the relation of $M$-equivalence”, Russian Math. Surveys, 39:6 (1984), 223–224
4. A.V. Arhangel'skiǐ, “On biradial topological spaces and groups”, Topology and its Applications, 36:2 (1990), 173
5. A.V. Arhangel'skiǐ, A.P. Kombarov, “On ∇-normal spaces”, Topology and its Applications, 35:2-3 (1990), 121
6. Vladimir G. Pestov, “Universal arrows to forgetful functors from categories of topological algebra”, BAZ, 48:2 (1993), 209
7. Vladimir Pestov, “A remark on embedding topological groups into products”, BAZ, 49:3 (1994), 519
8. Michael G. Tkačenko, “Free topological groups and inductive limits”, Topology and its Applications, 60:1 (1994), 1
9. Vladimir Pestov, “Free Abelian topological groups and the Pontryagin-Van Kampen duality”, BAZ, 52:2 (1995), 297
10. A.V. Arhangel'skiǐ, P.J. Collins, “On submaximal spaces”, Topology and its Applications, 64:3 (1995), 219
11. A.V. Arhangel'skii, “On Lindelöf property and spread in Cp-theory”, Topology and its Applications, 74:1-3 (1996), 83
12. Oleg Okunev, “Homeomorphisms of function spaces and hereditary cardinal invariants”, Topology and its Applications, 80:1-2 (1997), 177
13. S. A. Morris, V. Pestov, “A topological generalization of the HigmanNeumannNeumann theorem”, jgth, 1:2 (1998), 181
14. Mikhail Tkačenko, “Introduction to topological groups”, Topology and its Applications, 86:3 (1998), 179
15. Dmitri Shakhmatov, “A comparative survey of selected results and open problems concerning topological groups, fields and vector spaces”, Topology and its Applications, 91:1 (1999), 51
16. O. V. Sipacheva, “The topology of free topological groups”, J. Math. Sci., 131:4 (2005), 5765–5838
17. Peter Nickolas, Mikhail Tkachenko, “Local compactness in free topological groups”, BAZ, 68:2 (2003), 243
18. Alexander Arhangel'skii, “Topological vector spaces, compacta, and unions of subspaces”, Journal of Mathematical Analysis and Applications, 350:2 (2009), 616
19. A.V. Arhangel'skii, “-points in remainders of topological groups and some addition theorems in compacta”, Topology and its Applications, 156:12 (2009), 2013
20. M. Bruguera, M. Tkachenko, “Pontryagin duality in the class of precompact Abelian groups and the Baire property”, Journal of Pure and Applied Algebra, 2012
21. O.T.. Alas, V.V.. Tkachuk, R.G.. Wilson, “Maximal pseudocompact spaces and the Preiss-Simon property”, centr.eur.j.math, 12:3 (2014), 500
22. M. Hrušák, U.A. Ramos-García, “Malykhin's problem”, Advances in Mathematics, 262 (2014), 193
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