| Title:
|
Remarks on monotonically star compact spaces (English) |
| Author:
|
Singh, Sumit |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
147 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
319-323 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A space $ X $ is said to be monotonically star compact if one assigns to each open cover $ \mathcal {U} $ a subspace $ s(\mathcal {U}) \subseteq X $, called a kernel, such that $ s(\mathcal {U}) $ is a compact subset of $ X $ and $ {\rm St}(s(\mathcal {U}),\mathcal {U})=X $, and if $ \mathcal {V} $ refines $ \mathcal {U} $ then $ s(\mathcal {U}) \subseteq s(\mathcal {V}) $, where $ {\rm St}(s(\mathcal {U}),\mathcal {U})= \bigcup \{U \in \nobreak \mathcal {U}\colon U \cap s(\mathcal {U}) \not = \emptyset \} $. We prove the following statements: \item {(1)} The inverse image of a monotonically star compact space under the open perfect map is monotonically star compact. \item {(2)} The product of a monotonically star compact space and a compact space is monotonically star compact. \item {(3)} If $ X $ is monotonically star compact space with $ e(X) < \omega $, then $ A(X) $ is monotonically star compact, where $ A(X) $ is the Alexandorff duplicate of space $X$. \endgraf The above statement (2) gives an answer to the question of Song (2015). (English) |
| Keyword:
|
monotonically star compact |
| Keyword:
|
regular closed |
| Keyword:
|
perfect |
| Keyword:
|
star-compact |
| Keyword:
|
covering |
| Keyword:
|
star-covering |
| Keyword:
|
topological space |
| MSC:
|
54D20 |
| MSC:
|
54D30 |
| MSC:
|
54D40 |
| idZBL:
|
Zbl 07584127 |
| idMR:
|
MR4482308 |
| DOI:
|
10.21136/MB.2021.0158-20 |
| . |
| Date available:
|
2022-09-05T09:36:49Z |
| Last updated:
|
2022-12-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151010 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[10] Song, Y. -K.: Monotonically star compact spaces.Topology Appl. 190 (2015), 35-41 \99999DOI99999 10.1016/j.topol.2015.04.016 . Zbl 1316.54010, MR 3349504 |
| Reference:
|
[11] Xuan, W. -F., Shi, W. -X.: Notes on star Lindelöf spaces.Topology Appl. 204 (2016), 63-69. Zbl 1342.54015, MR 3482703, 10.1016/j.topol.2016.02.009 |
| . |
