Souslin property in free topological groups on bicompacta (Q790958)

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 \(c(G)\leq \aleph_ 0\).