Bulletin of the Belgian Mathematical Society - Simon Stevin

On compactly-fibered coset spaces

Hanfeng Wang and Wei He

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Abstract

Topological properties of compactly-fibered coset spaces are investigated. It is proved that for a compactly-fibered coset space $X$ with $Nag(X)\leq\tau$, the closure of a family of $G_{\tau}$-sets is also a $G_{\tau}$-set in $X$. We also show that the equation $\chi(X)=\pi\chi(X)$ holds for any compactly-fibered coset space $X$. A Dichotomy Theorem for compactly-fibered coset spaces is established: every remainder of such a space has the Baire property, or is $\sigma$-compact.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 26, Number 3 (2019), 401-411.

Dates
First available in Project Euclid: 17 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1568685654

Digital Object Identifier
doi:10.36045/bbms/1568685654

Mathematical Reviews number (MathSciNet)
MR4007605

Zentralblatt MATH identifier
07120722

Subjects
Primary: 54D40: Remainders 54E35: Metric spaces, metrizability 22A05: Structure of general topological groups

Keywords
compactly-fibered coset space Nagami number remainder $G_{\tau}$-set metrizable

Citation

Wang, Hanfeng; He, Wei. On compactly-fibered coset spaces. Bull. Belg. Math. Soc. Simon Stevin 26 (2019), no. 3, 401--411. doi:10.36045/bbms/1568685654. https://projecteuclid.org/euclid.bbms/1568685654


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