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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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

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

First available in Project Euclid: 11 September 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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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