STRUCTURE AND CLASSIFICATION OF TOPOLOGICAL SPACES AND CARDINAL INVARIANTS

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 -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 ksubgroup. This result is specific for topological groups: under Martin Axiom there exists a sequential topologically homogeneous k-space X with 0 = cs * (X) < (X).

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