Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

Version 1 : Received: 21 July 2021 / Approved: 21 July 2021 / Online: 21 July 2021 (10:37:18 CEST)

How to cite: Tkachenko, M. Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups. Preprints 2021, 2021070483 (doi: 10.20944/preprints202107.0483.v1). Tkachenko, M. Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups. Preprints 2021, 2021070483 (doi: 10.20944/preprints202107.0483.v1).

Abstract

We study factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let $D=\prod_{i\in I}D_i$ be a product of paratopological groups, $S$ be a dense subgroup of $D$, and $\chi$ a continuous character of $S$. Then one can find a finite set $E\subset I$ and continuous characters $\chi_i$ of $D_i$, for $i\in E$, such that $\chi=\big(\prod_{i\in E} \chi_i\circ p_i\big)\hs1\res\hs1 S$, where $p_i\colon D\to D_i$ is the projection.

Keywords

Monoid; Group; Character; Homomorphism; Factorization; Roelcke uniformity

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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