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Compact condensations of Hausdorff spaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 09 Feb 2021Embargo end date: 01 Jan 2020 Russian Federation Publisher:Springer Science and Business Media LLCJournal:Acta Mathematica Hungarica, volume 164, pages 15-27 (issn: 0236-5294, eissn: 1588-2632, Copyright policy )
Authors: Alexander V. Osipov; Alexander V. Osipov; E. G. Pytkeev; V. I. Belugin;

doi: 10.1007/s10474-021-01131-z , 10.48550/arxiv.2007.12373

arXiv: http://arxiv.org/abs/2007.12373

Compact condensations of Hausdorff spaces

Abstract

In this paper, we continue to study one of the classic problems in general topology raised by P.S. Alexandrov: when a Hausdorff space $X$ has a continuous bijection (a condensation) onto a compactum? We concentrate on the situation when not only $X$ but also $X\setminus Y$ can be condensed onto a compactum whenever the cardinality of $Y$ does not exceed certain $��$.

17 pages

Country
Russian Federation
Related Organizations
Keywords

CONDENSATION, CONTINUOUS DECOMPOSITION, WEAKLY DYADIC COMPACT, General Topology (math.GN), FOS: Mathematics, AΤ-SPACE, SUBCOMPACT SPACE, Mathematics - General Topology

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Average
Top 10%
Green
bronze