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

This article is cited in 24 scientific papers (total in 24 papers)

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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
\by A.~V.~Arkhangel'skii
\paper Relations among the invariants of topological groups and their subspaces
\jour Uspekhi Mat. Nauk
\yr 1980
\vol 35
\issue 3(213)
\pages 3--22
\jour Russian Math. Surveys
\yr 1980
\vol 35
\issue 3
\pages 1--23

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    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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. V. Tkachuk, “On a method of constructing examples of $M$-equivalent spaces”, Russian Math. Surveys, 38:6 (1983), 135–136  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. V. G. Pestov, “Some topological properties preserved by the relation of $M$-equivalence”, Russian Math. Surveys, 39:6 (1984), 223–224  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A.V. Arhangel'skiǐ, “On biradial topological spaces and groups”, Topology and its Applications, 36:2 (1990), 173  crossref
    5. A.V. Arhangel'skiǐ, A.P. Kombarov, “On ∇-normal spaces”, Topology and its Applications, 35:2-3 (1990), 121  crossref
    6. Vladimir G. Pestov, “Universal arrows to forgetful functors from categories of topological algebra”, BAZ, 48:2 (1993), 209  crossref  mathscinet  zmath  isi
    7. Vladimir Pestov, “A remark on embedding topological groups into products”, BAZ, 49:3 (1994), 519  crossref  mathscinet  zmath  isi
    8. Michael G. Tkačenko, “Free topological groups and inductive limits”, Topology and its Applications, 60:1 (1994), 1  crossref
    9. Vladimir Pestov, “Free Abelian topological groups and the Pontryagin-Van Kampen duality”, BAZ, 52:2 (1995), 297  crossref  mathscinet  zmath  isi
    10. A.V. Arhangel'skiǐ, P.J. Collins, “On submaximal spaces”, Topology and its Applications, 64:3 (1995), 219  crossref
    11. A.V. Arhangel'skii, “On Lindelöf property and spread in Cp-theory”, Topology and its Applications, 74:1-3 (1996), 83  crossref
    12. Oleg Okunev, “Homeomorphisms of function spaces and hereditary cardinal invariants”, Topology and its Applications, 80:1-2 (1997), 177  crossref
    13. S. A. Morris, V. Pestov, “A topological generalization of the HigmanNeumannNeumann theorem”, jgth, 1:2 (1998), 181  crossref  mathscinet  zmath  isi
    14. Mikhail Tkačenko, “Introduction to topological groups”, Topology and its Applications, 86:3 (1998), 179  crossref
    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  crossref
    16. O. V. Sipacheva, “The topology of free topological groups”, J. Math. Sci., 131:4 (2005), 5765–5838  mathnet  crossref  mathscinet  zmath  elib  elib
    17. Peter Nickolas, Mikhail Tkachenko, “Local compactness in free topological groups”, BAZ, 68:2 (2003), 243  crossref  mathscinet  zmath  isi  elib
    18. Alexander Arhangel'skii, “Topological vector spaces, compacta, and unions of subspaces”, Journal of Mathematical Analysis and Applications, 350:2 (2009), 616  crossref
    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  crossref
    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  crossref
    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  crossref
    22. M. Hrušák, U.A. Ramos-García, “Malykhin's problem”, Advances in Mathematics, 262 (2014), 193  crossref
    23. Iván Sánchez, “Paratopological groups with a <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="" xmlns:xs="" xmlns:xsi="" xmlns="" xmlns:ja="" xmlns:mml="" xmlns:tb="" xmlns:sb="" xmlns:ce="" xmlns:xlink="" xmlns:cals="" xmlns:sa=""><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mi>δ</mml:mi></mml:mrow></mml:msub></mml:math>-diagonal of infinite rank”, Topology and its Applications, 178 (2014), 459  crossref
    24. Iván Sánchez, “Condensations of paratopological groups”, Topology and its Applications, 180 (2015), 124  crossref
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