| Title:
|
Convergence in compacta and linear Lindelöfness (English) |
| Author:
|
Arhangel'skii, A. V. |
| Author:
|
Buzyakova, R. Z. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
159-166 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a compact Hausdorff space with a point $x$ such that $X\setminus \{ x\}$ is linearly Lindelöf. Is then $X$ first countable at $x$? What if this is true for every $x$ in $X$? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is ``yes'' when $X$ is, in addition, $\omega $-monolithic. We also prove that if $X$ is compact, Hausdorff, and $X\setminus \{ x\}$ is strongly discretely Lindelöf, for every $x$ in $X$, then $X$ is first countable. An example of linearly Lindelöf hereditarily realcompact non-Lindelöf space is constructed. Some intriguing open problems are formulated. (English) |
| Keyword:
|
point of complete accumulation |
| Keyword:
|
linearly Lindelöf space |
| Keyword:
|
local compactness |
| Keyword:
|
first countability |
| Keyword:
|
$\kappa $-accessible diagonal |
| MSC:
|
54A25 |
| MSC:
|
54D30 |
| MSC:
|
54E35 |
| MSC:
|
54F99 |
| idZBL:
|
Zbl 0937.54022 |
| idMR:
|
MR1623006 |
| . |
| Date available:
|
2009-01-08T18:39:45Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118994 |
| . |
| 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:
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| Reference:
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| . |
