| Title:
|
On Hattori spaces (English) |
| Author:
|
Bouziad, A. |
| Author:
|
Sukhacheva, E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
58 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
213-223 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a subset $A$ of the real line $\mathbb R$, Hattori space $H(A)$ is a topological space whose underlying point set is the reals $\mathbb R$ and whose topology is defined as follows: points from $A$ are given the usual Euclidean neighborhoods while remaining points are given the neighborhoods of the Sorgenfrey line. In this paper, among other things, we give conditions on $A$ which are sufficient and necessary for $H(A)$ to be respectively almost Čech-complete, Čech-complete, quasicomplete, Čech-analytic and weakly separated (in Tkacenko sense). Some of these results solve questions raised by V.A. Chatyrko and Y. Hattori. (English) |
| Keyword:
|
Hattori space |
| Keyword:
|
Čech-complete space |
| Keyword:
|
Čech-analytic space |
| Keyword:
|
neighborhood assignment |
| Keyword:
|
Sorgenfrey line |
| Keyword:
|
scattered set |
| Keyword:
|
weakly separated space |
| MSC:
|
54C05 |
| MSC:
|
54C35 |
| MSC:
|
54C45 |
| MSC:
|
54C99 |
| idZBL:
|
Zbl 06773715 |
| idMR:
|
MR3666942 |
| DOI:
|
10.14712/1213-7243.2015.199 |
| . |
| Date available:
|
2017-06-13T13:23:39Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146789 |
| . |
| 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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| . |
