| | |
| | |
Stat |
Members: 3643 Articles: 2'487'895 Articles rated: 2609
29 March 2024 |
|
| | | |
|
Article overview
| |
|
On closed embeddings of free topological algebras | T.Banakh
; O.Hryniv
; | Date: |
20 Feb 2012 | Abstract: | Let $mathcal K$ be a complete quasivariety of completely regular universal
topological algebras of continuous signature $mathcal E$ (which means that
$mathcal K$ is closed under taking subalgebras, Cartesian products, and
includes all completely regular topological $mathcal E$-algebras algebraically
isomorphic to members of $mathcal K$). For a topological space $X$ by $F(X)$
we denote the free universal $mathcal E$-algebra over $X$ in the class
$mathcal K$. Using some extension properties of the Hartman-Mycielski
construction we prove that for a closed subspace $X$ of a metrizable (more
generally, stratifiable) space $Y$ the induced homomorphism $F(X) o F(Y)$
between the respective free universal algebras is a closed topological
embedding. This generalizes one result of V.Uspenskii concerning embeddings of
free topological groups. | Source: | arXiv, 1202.4480 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |