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Homogeneity Problems in the Theory of Čech Compactifications

In: The Mathematical Legacy of Eduard Čech

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  • Walter Rudin

    (University of Rochester)

Abstract

If X is a completely regular topological space, there exists a space ßX, the so-called Cech compactification of X, which is characterized by the following three properties: ßX is a compact (bicompact, in the older terminology) Hausdorff space, X is a dense subset of ßX, and every bounded continuous real-valued function on X can be extended to a continuous function on βX [1; 831].

Suggested Citation

  • Walter Rudin, 1993. "Homogeneity Problems in the Theory of Čech Compactifications," Springer Books, in: Miroslav Katětov & Petr Simon (ed.), The Mathematical Legacy of Eduard Čech, pages 81-92, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-7524-0_7
    DOI: 10.1007/978-3-0348-7524-0_7
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