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

By Taras Banak, Lubomyr Zdomskyi. 2004

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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 @-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 k!- subgroup. This result is specific for topological groups: under Martin Axiom there exists a sequential topologically homogeneous k!-space X with @0 = cs* Â(X) < A(X).

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8bd1e61fe177a4bb7ac2efbe75d0bf205676c323