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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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Russian Mathematical Surveys, 1980, 35:3, 1–23
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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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V. G. Pestov, “Some topological properties preserved by the relation of $M$-equivalence”, Russian Math. Surveys, 39:6 (1984), 223–224
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A.V. Arhangel'skiǐ, “On biradial topological spaces and groups”, Topology and its Applications, 36:2 (1990), 173
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Vladimir G. Pestov, “Universal arrows to forgetful functors from categories of topological algebra”, BAZ, 48:2 (1993), 209
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Vladimir Pestov, “Free Abelian topological groups and the Pontryagin-Van Kampen duality”, BAZ, 52:2 (1995), 297
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S. A. Morris, V. Pestov, “A topological generalization of the HigmanNeumannNeumann theorem”, jgth, 1:2 (1998), 181
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Mikhail Tkačenko, “Introduction to topological groups”, Topology and its Applications, 86:3 (1998), 179
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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
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O. V. Sipacheva, “The topology of free topological groups”, J. Math. Sci., 131:4 (2005), 5765–5838
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