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Souslin property in free topological groups on bicompacta. (English. Russian original) Zbl 0535.22002
Math. Notes 34, 790-793 (1983); translation from Mat. Zametki 34, No. 4, 601-607 (1983).
Let X be a completely regular space and F(X) be its free Markov topological group. It is shown that if X is a pseudocompact space then \(c(F(X))\leq \aleph_ 0\), i.e. any disjoint system of open sets of G is not uncountable. In particular, if a topological group G is \(\sigma\)- compact or G is topologically generated by a compact set then \(c(G)\leq \aleph_ 0\).
Reviewer: I.V.Protasov

MSC:
22A05 Structure of general topological groups
54F99 Special properties of topological spaces
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