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Bounded Subsets of Tychonoff Spaces: A Survey of Results and Problems

  • M. Sanchis
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 55)

Abstract

Throughout, all spaces are by default Tychonoff. A subset B of a space X is said to be bounded (in X) if every real-valued continuous function on X is bounded on B. A first consequence of the definition is that boundedness generalizes pseudocompactness. Indeed, a space X is pseudocompact if and only if it is bounded in itself. Nevertheless, in interpreting this conclusion, caution must be exercised. Notice that every subset B of a (pseudo)compact space X is bounded.

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Authors and Affiliations

  1. 1.Institut de Matemàtiques i Aplicacions de Castelló, Universitat Jaume I de CastellóCastellón de la PlanaSpain

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