## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On compactly-fibered coset spaces

#### 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

https://projecteuclid.org/euclid.bbms/1568685654

Digital Object Identifier
doi:10.36045/bbms/1568685654

Mathematical Reviews number (MathSciNet)
MR4007605

Zentralblatt MATH identifier
07120722

#### 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