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

• Banak, Taras ^[2] ; Zdomskyi, Lubomyr ^[1]
  1. [1] National University

     National University

     Estados Unidos

     
  2. [2] Akademia Swietorzyska
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 5, Nº. 1, 2004, págs. 25-48
• Idioma: inglés
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• Resumen

  • 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).