Bulletin of the Belgian Mathematical Society - Simon Stevin

Polish factorizations, cosmic spaces and domain representability

Jila Niknejad, Vladimir V. Tkachuk, and Lynne Yengulalp

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Abstract

We say that a space $X$ is {\it cofinally Polish} if for every continuous onto map $f:X\to M$ of $X$ onto a separable metrizable space $M$, there exists a Polish space $P$ and continuous onto maps $g:X\to P$ and $h:P\to M$ such that $f=h\circ g$. We study general properties of cofinally Polish spaces and compare the property of being cofinally Polish with subcompactness and domain representability. It is established, among other things, that a space with a countable network is cofinally Polish if and only if it is domain representable. We also show that any $G_\delta$-subset of an Eberlein compact space must be subcompact thus giving an answer to an open problem published in 2013.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 3 (2018), 439-452.

Dates
First available in Project Euclid: 11 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1536631237

Mathematical Reviews number (MathSciNet)
MR3852678

Zentralblatt MATH identifier
06970024

Subjects
Primary: 54E52: Baire category, Baire spaces
Secondary: 54E20: Stratifiable spaces, cosmic spaces, etc. 54C05: Continuous maps 54C35: Function spaces [See also 46Exx, 58D15]

Keywords
Polish spaces factorization cofinally Polish spaces cosmic spaces domain representability subcompact spaces Eberlein compact spaces

Citation

Niknejad, Jila; Tkachuk, Vladimir V.; Yengulalp, Lynne. Polish factorizations, cosmic spaces and domain representability. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 3, 439--452. https://projecteuclid.org/euclid.bbms/1536631237


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