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. Preprints2021, 2021070483. https://doi.org/10.20944/preprints202107.0483.v1
Tkachenko, M. Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups. Preprints 2021, 2021070483. https://doi.org/10.20944/preprints202107.0483.v1
Tkachenko, M. Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups. Preprints2021, 2021070483. https://doi.org/10.20944/preprints202107.0483.v1
APA Style
Tkachenko, M. (2021). Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups. Preprints. https://doi.org/10.20944/preprints202107.0483.v1
Chicago/Turabian Style
Tkachenko, M. 2021 "Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups" Preprints. https://doi.org/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.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
