| Title:
|
A note on functional tightness and minitightness of space of the $G$-permutation degree (English) |
| Author:
|
Georgiou, Dimitrios N. |
| Author:
|
Mamadaliev, Nodirbek K. |
| Author:
|
Zhuraev, Rustam M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
64 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
97-108 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the behavior of the minimal tightness and functional tightness of topological spaces under the influence of the functor of the permutation degree. Analytically: a) We introduce the notion of $\tau$-open sets and investigate some basic properties of them. b) We prove that if the map $f\colon X\rightarrow Y$ is $\tau$-continuous, then the map $SP^{n}f\colon SP^n X \rightarrow SP^n Y$ is also $\tau$-continuous. c) We show that the functor $SP^n$ preserves the functional tightness and the minimal tightness of compacts. d) Finally, we give some facts and properties on $\tau$-bounded spaces. More precisely, we prove that the functor of permutation degree $SP^n$ preserves the property of being $\tau$-bounded. (English) |
| Keyword:
|
$\tau$-open set |
| Keyword:
|
$\tau$-bounded space |
| Keyword:
|
functional tightness |
| Keyword:
|
minimal tightness |
| MSC:
|
54B20 |
| MSC:
|
54C05 |
| idZBL:
|
Zbl 07790585 |
| idMR:
|
MR4631793 |
| DOI:
|
10.14712/1213-7243.2023.019 |
| . |
| Date available:
|
2023-08-28T09:48:46Z |
| Last updated:
|
2025-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151802 |
| . |
| Reference:
|
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