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Variations on ω-boundedness

Israel Journal of Mathematics volume 194, pages 745–766 (2013)Cite this article

Abstract

Let be a property (or, equivalently, a class) of topological spaces. A space X is called -bounded if every subspace of X with (or in) has compact closure. Thus, countable-bounded has been known as ω-bounded and (σ-compact)-bounded as strongly ω-bounded.

In this paper we present a systematic study of the interrelations of these two known “boundedness” concepts with -boundedness where is one of the further countability properties weakly Lindelöf, Lindelöf, hereditarily Lindelöf, and ccc.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, H-1053, Budapest, Hungary

    Istvan Juhász

  2. Faculty of Sciences, Department of Mathematics, VU University Amsterdam, 1081 HV, Amsterdam, The Netherlands

    Jan van Mill

  3. Department of Mathematics, University of Toronto, Toronto, Ontario, Canada, M5S 2E4

    William Weiss

Authors
  1. Istvan Juhász
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  2. Jan van Mill
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  3. William Weiss
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Corresponding author

Correspondence to Istvan Juhász.

Additional information

The first author was supported by OTKA grants no. 68262 and 83726.

The second and third author are pleased to thank the Alfréd Rényi Institute of Mathematics for generous hospitality.

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Juhász, I., van Mill, J. & Weiss, W. Variations on ω-boundedness. Isr. J. Math. 194, 745–766 (2013). https://doi.org/10.1007/s11856-012-0062-8

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  • DOI: https://doi.org/10.1007/s11856-012-0062-8

Keywords

  • Compact Space
  • Continuum Hypothesis
  • Nonempty Open Subset
  • Compact Closure
  • Clopen Subset