| Title:
|
$T_{2}$ and $T_{3}$ objects at $p$ in the category of proximity spaces (English) |
| Author:
|
Kula, Muammer |
| Author:
|
Özkan, Samed |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
145 |
| Issue:
|
2 |
| Year:
|
2020 |
| Pages:
|
177-190 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In previous papers, various notions of pre-Hausdorff, Hausdorff and regular objects at a point $p$ in a topological category were introduced and compared. The main objective of this paper is to characterize each of these notions of pre-Hausdorff, Hausdorff and regular objects locally in the category of proximity spaces. Furthermore, the relationships that arise among the various ${\rm Pre}T_{2}$, $T_{i}$, $i=0,1,2,3$, structures at a point $p$ are investigated. Finally, we examine the relationships between the generalized separation properties and the separation properties at a point $p$ in this category. (English) |
| Keyword:
|
topological category |
| Keyword:
|
proximity space |
| Keyword:
|
Hausdorff space |
| Keyword:
|
regular space |
| MSC:
|
18B99 |
| MSC:
|
54B30 |
| MSC:
|
54D10 |
| MSC:
|
54E05 |
| idZBL:
|
07217188 |
| idMR:
|
MR4221828 |
| DOI:
|
10.21136/MB.2019.0144-17 |
| . |
| Date available:
|
2020-06-10T13:16:24Z |
| Last updated:
|
2021-04-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148153 |
| . |
| Reference:
|
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