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


  • Taras Banak Akademia Swietorzyska
  • Lubomyr Zdomskyi Ivan Franko Lviv National University



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


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).


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How to Cite

T. Banak and L. Zdomskyi, “The topological structure of (homogeneous) spaces and groups with countable cs∗-character”, Appl. Gen. Topol., vol. 5, no. 1, pp. 25–48, Apr. 2004.



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