Open AccessThe topological structure of (homogeneous) spaces and groups with countable cs∗-character
Author(s) -
Taras Banak,
Lubomyr Zdomskyi
Publication year - 2004
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 13
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2004.1993
Subject(s) - mathematics , topological group , countable set , metrization theorem , topological space , character (mathematics) , group (periodic table) , topology (electrical circuits) , connected space , isolated point , second countable space , pure mathematics , discrete mathematics , topological vector space , combinatorics , separable space , mathematical analysis , geometry , chemistry , organic chemistry
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 = cs∗x (X) <ψ (X)