# zbMATH — the first resource for mathematics

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
##### Keywords:
free Markov topological group; Suslin number
Full Text:
##### References:
 [1] L. N. Ivanovskii, ?On a conjecture of P. S. Aleksandrov,? Dokl. Akad. Nauk SSSR,123, No. 5, 785-786 (1958). [2] V. Kuz’minov, ?On a conjecture of P. S. Aleksandrov in the theory of topological groups,? Dokl. Akad. Nauk SSSR,125, No. 4, 727-729 (1959). [3] A. Weil, ?Sur les espaces a structure uniforme et sur la topologie générale,? Actualites Sci. Ind., 551, Hermann Cie, Paris (1938). · Zbl 0019.18604 [4] M. E. Rudin, Lectures on Set Theoretic Topology, Providence, Rhode Island (1975). · Zbl 0318.54001 [5] V. G. Pestov, ?Some properties of free topological groups,? Mat., Mekh., No. 1, 35-37 (1982) · Zbl 0499.22001 [6] A. V. Arkhangel’skii, ?On relationships between invariants of topological groups and their subspaces,? Usp. Mat. Nauk,35, No. 3, 3-22 (1980).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.