Bulletin of the Belgian Mathematical Society - Simon Stevin

The $\tau$-precompact Hausdorff Group Reflection of Topological Groups

Wei Hei and Zhiqiang Xiao

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Abstract

We give three different descriptions of the $\tau$-precompact Hausdorff group reflection of topological groups. In particular, we describe the $\omega$-narrow Hausdorff reflection of a given topological group. We also prove that the $\tau$-precompact Hausdorff reflection functor preserves perfect surjective homomorphisms, quotient homomorphisms and arbitrary products. As a direct application, we deduce that the compact Hausdorff reflection functor preserves arbitrary products.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 1 (2018), 107-120.

Dates
First available in Project Euclid: 11 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1523412056

Digital Object Identifier
doi:10.36045/bbms/1523412056

Mathematical Reviews number (MathSciNet)
MR3784509

Subjects
Primary: 22A05: Structure of general topological groups 54H11: Topological groups [See also 22A05] 18B99: None of the above, but in this section

Keywords
$\tau$-precompact Hausdorff group reflection $\omega$-narrow Hausdorff group reflection $\tau$-precompact Hausdorff reflection functor

Citation

Hei, Wei; Xiao, Zhiqiang. The $\tau$-precompact Hausdorff Group Reflection of Topological Groups. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 1, 107--120. doi:10.36045/bbms/1523412056. https://projecteuclid.org/euclid.bbms/1523412056


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