The topological structure of (homogeneous) spaces and groups with countable csâˆ—-character

Taras Banak; Lubomyr Zdomskyi

doi:10.4995/agt.2004.1993

Authors

Taras Banak Akademia Swietorzyska
Lubomyr Zdomskyi Ivan Franko Lviv National University

DOI:

https://doi.org/10.4995/agt.2004.1993

Keywords:

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

Abstract

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

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