Bulletin of the Belgian Mathematical Society - Simon Stevin

Notes on Remainders of Paratopological Groups

Hanfeng Wang and Wei He

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Abstract

In this paper, it is proved that a non-locally compact paratopological group $G$ has a remainder which is a $p$-space if and only if $G$ is either a Lindelöf $p$-space or a $\sigma$-compact space. We show that if $G$ is a non-locally compact paratopological group with a compactification $bG$ such that the remainder $bG\setminus G$ is locally metrizable, then both $G$ and $bG$ are separable and metrizable. It is proved that if $G$ is a cosmic paratopological group with a paracompact remainder, then $G$ is separable and metrizable.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 3 (2014), 479-488.

Dates
First available in Project Euclid: 11 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1407765885

Digital Object Identifier
doi:10.36045/bbms/1407765885

Mathematical Reviews number (MathSciNet)
MR3250774

Zentralblatt MATH identifier
1301.54040

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

Keywords
remainder paratopological group compactification metrizable $p$-space $\pi$-character

Citation

Wang, Hanfeng; He, Wei. Notes on Remainders of Paratopological Groups. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 3, 479--488. doi:10.36045/bbms/1407765885. https://projecteuclid.org/euclid.bbms/1407765885


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