| Title:
|
Addition theorems, $D$-spaces and dually discrete spaces (English) |
| Author:
|
Alas, Ofelia T. |
| Author:
|
Tkachuk, Vladimir V. |
| Author:
|
Wilson, Richard G. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
113-124 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A {\it neighbourhood assignment\/} in a space $X$ is a family $\Cal O= \{O_x:x\in X\}$ of open subsets of $X$ such that $x\in O_x$ for any $x\in X$. A set $Y\subseteq X$ is {\it a kernel of $\Cal O$\/} if $\Cal O(Y)=\bigcup\{O_x:x\in Y\}=X$. If every neighbourhood assignment in $X$ has a closed and discrete (respectively, discrete) kernel, then $X$ is said to be a $D$-space (respectively a dually discrete space). In this paper we show among other things that every GO-space is dually discrete, every subparacompact scattered space and every continuous image of a Lindelöf $P$-space is a $D$-space and we prove an addition theorem for metalindelöf spaces which answers a question of Arhangel'skii and Buzyakova. (English) |
| Keyword:
|
neighbourhood assignment |
| Keyword:
|
$D$-space |
| Keyword:
|
dually discrete space |
| Keyword:
|
discrete kernel |
| Keyword:
|
scattered space |
| Keyword:
|
paracompactness |
| Keyword:
|
GO-space |
| MSC:
|
54D20 |
| MSC:
|
54G99 |
| idZBL:
|
Zbl 1212.54074 |
| idMR:
|
MR2562808 |
| . |
| Date available:
|
2009-08-18T12:23:33Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133419 |
| . |
| 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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