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Acta Mathematica Hungarica

, Volume 159, Issue 2, pp 674–688 | Cite as

Cellular-compact spaces and their applications

  • V. V. TkachukEmail author
  • R. G. Wilson
Article

Abstract

We introduce the notion of a cellular-compact space and prove that cellular compactness is a nice property that implies cellular Lindelöfness. The class of cellular-compact spaces is preserved by continuous images and finite unions, as well as by regular closed subsets and extensions. It is established that cellular-compact spaces must be pseudocompact but not necessarily countably compact. We prove that first countable cellular-compact regular spaces are countably compact and their cardinality does not exceed \({2^{\omega}}\). We also show that a collectionwise normal Fréchet–Urysohn cellular-compact space need not be compact and there exist Fréchet–Urysohn cellular-compact spaces that do not have a dense countably compact subspace.

Key words and phrases

cellular-compact space cellular-Lindelöf space weakly Lindelöf space disjoint local \(\pi\)-base first countable space maximal cellular-compact space 

Mathematics Subject Classification

primary 54D20 54D99 secondary 54D55 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad Autónoma MetropolitanaMexico D.F.Mexico

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