### The topological structure of (homogeneous) spaces and groups with countable cs*-characterThe topological structure of (homogeneous) spaces and groups with countable cs*-character

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 Author Banakh, Taras ♦ Zdomskyy, Lyubomyr Source arXiv.org Content type Text File Format PDF Date of Submission 2009-11-20 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - General Topology ♦ Mathematics - Group Theory ♦ 54H11 ♦ 54A35 ♦ 54A25 ♦ 54D55 ♦ 22A05 ♦ 54A20 ♦ math 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 aleph-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 $k_\omega$-subgroup. Description Reference: Appl. Gen. Top. 5:1 (2004), 25--48 Educational Use Research Learning Resource Type Article