| Title:
|
Relative normality and product spaces (English) |
| Author:
|
Hoshina, Takao |
| Author:
|
Sokei, Ryoken |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
515-524 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Arhangel'ski\u{\i} defines in [Topology Appl. 70 (1996), 87--99], as one of various notions on relative topological properties, strong normality of $A$ in $X$ for a subspace $A$ of a topological space $X$, and shows that this is equivalent to normality of $X_A$, where $X_A$ denotes the space obtained from $X$ by making each point of $X \setminus A$ isolated. In this paper we investigate for a space $X$, its subspace $A$ and a space $Y$ the normality of the product $X_A \times Y$ in connection with the normality of $(X\times Y)_{(A\times Y)}$. The cases for paracompactness, more generally, for $\gamma$-paracompactness will also be discussed for $X_A\times Y$. As an application, we prove that for a metric space $X$ with $A \subset X$ and a countably paracompact normal space $Y$, $X_A \times Y$ is normal if and only if $X_A \times Y$ is countably paracompact. (English) |
| Keyword:
|
strongly normal in |
| Keyword:
|
normal |
| Keyword:
|
$\gamma$-paracompact |
| Keyword:
|
product spaces |
| Keyword:
|
\newline weak $C$-embedding |
| MSC:
|
54B05 |
| MSC:
|
54B10 |
| MSC:
|
54C20 |
| MSC:
|
54C45 |
| MSC:
|
54D15 |
| MSC:
|
54D20 |
| idZBL:
|
Zbl 1097.54013 |
| idMR:
|
MR2025817 |
| . |
| Date available:
|
2009-01-08T19:30:48Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119405 |
| . |
| 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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| . |
