Year: 2021
Type: preprint
Abstract: Given a topological ring $R$, we study semitopological $R$-modules, construct their completions, Bohr and borno modifications. For every topological space $X$, we construct the free (semi)topological $R$-module over $X$ and prove that for a $k$-space $X$ its free semitopological $R$-module is a topological $R$-module. Also we construct a Tychonoff space $X$ whose free semitopological $R$-module is not a topological $R$-module.
Source: arXiv (Cornell University)
Authors: Banakh, Taras, Ravsky, Alex
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4287212938