The topological structure of (homogeneous) spaces and groups with countable cs∗-character

Taras Banak, Lubomyr Zdomskyi

Abstract

In this paper we introduce and study three new cardinal topological invariants called the cs-, cs-, and sb-characters. The class of topological spaces with countable cs-character is closed under many topological operations and contains all N-spaces and all spaces with point-countable cs-network. Our principal result states that each non-metrizable sequential topological group with countable cs- character has countable pseudo-character and contains an open kω- subgroup. This result is specific for topological groups: under Martin Axiom there exists a sequential topologically homogeneous kω-space X with N0 = csx ­(X) <ψ (X).


Keywords

sb-network; cs-networ;, cs∗-network; Sequential topological group; kω-group; Topologically homogeneous space; Small cardinal; Cardinal invariant

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