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Preserved in Portico This version is not peer-reviewed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)
A peer-reviewed article of this Preprint also exists.
Tkachenko, M.G. Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups. Axioms 2021, 10, 167, doi:10.3390/axioms10030167. Tkachenko, M.G. Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups. Axioms 2021, 10, 167, doi:10.3390/axioms10030167.
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
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.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment