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Weakly Pseudocompact Spaces

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Pseudocompact Topological Spaces

Part of the book series: Developments in Mathematics ((DEVM,volume 55))

Abstract

A well known result established by Hewitt (Trans Amer Math Soc 64:45–99 1948, [16]) states that a space X is pseudocompact if and only if X is \(G_\delta \)-dense in \(\beta X\). In García-Ferreira and García-Maynez (Houston J Math 20(1):145–159, 1994, [12]), S. García-Ferreira and A. García-Máynez introduced the following concept: a topological space is weakly pseudocompact if it is \(G_\delta \)-dense in one of its compactifications. Thus, every pseudocompact space is weakly pseudocompact.

The third author was supported by a grant given by PASPA-DGAPA-UNAM.

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Notes

  1. 1.

    In this Chapter, a perfect mapping is a continuous and closed function with compact fibers.

  2. 2.

    A topological group G is called precompact if for every neighborhood U of the identity in G one can find a finite set \(F\subset G\) such that \(FU=G\). An in-depth analysis of the relationships between pseudocompactness and topological groups can be found in Chap. 2 of this book.

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Author information

Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, Ehime University, Matsuyama, 790-8577, Japan

    A. Dorantes-Aldama

  2. Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, 72570, Puebla, México

    O. Okunev

  3. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510, Ciudad de México, México

    Á. Tamariz-Mascarúa

Authors
  1. A. Dorantes-Aldama
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  2. O. Okunev
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  3. Á. Tamariz-Mascarúa
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Corresponding author

Correspondence to Á. Tamariz-Mascarúa .

Editor information

Editors and Affiliations

  1. Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México-Campus Morelia, Morelia, Michoacán, Mexico

    Michael Hrušák

  2. Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad de México, Mexico

    Ángel Tamariz-Mascarúa

  3. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Ciudad de México, Mexico

    Mikhail Tkachenko

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Dorantes-Aldama, A., Okunev, O., Tamariz-Mascarúa, Á. (2018). Weakly Pseudocompact Spaces. In: Hrušák, M., Tamariz-Mascarúa, Á., Tkachenko, M. (eds) Pseudocompact Topological Spaces. Developments in Mathematics, vol 55. Springer, Cham. https://doi.org/10.1007/978-3-319-91680-4_5

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