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Topological Homogeneity

In: Recent Progress in General Topology III

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  • A. V. Arhangel’skii

  • J. van Mill

    (VU University Amsterdam, Department of Mathematics, Faculty of Sciences)

Abstract

This paper deals with homogeneous spaces that are not assumed to be close to a manifold; in fact, to homogeneous spaces on which very few assumptions are imposed and these assumptions are of quite general nature (like compactness). On the other hand, we also consider homogeneous spaces with some sort of pathology. There are many very interesting results on homogeneous metrizable continua which consequently will not be discussed here. It turns out that for the class of spaces we are interested in, many fundamental problems remain unsolved. Cardinal invariants and their theory are shown to be one of the main instruments in their study.

Suggested Citation

  • A. V. Arhangel’skii & J. van Mill, 2014. "Topological Homogeneity," Springer Books, in: K.P. Hart & J. van Mill & P. Simon (ed.), Recent Progress in General Topology III, edition 127, pages 1-68, Springer.
    • Handle: RePEc:spr:sprchp:978-94-6239-024-9_1
    DOI: 10.2991/978-94-6239-024-9_1
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