| Title:
|
Metrization of function spaces with the Fell topology (English) |
| Author:
|
Yang, Hanbiao |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
307-318 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a Tychonoff space $X$, let $\downarrow {\rm C}_F(X)$ be the family of hypographs of all continuous maps from $X$ to $[0,1]$ endowed with the Fell topology. It is proved that $X$ has a dense separable metrizable locally compact open subset if $\downarrow {\rm C}_F(X)$ is metrizable. Moreover, for a first-countable space $X$, $\downarrow {\rm C}_F(X)$ is metrizable if and only if $X$ itself is a locally compact separable metrizable space. There exists a Tychonoff space $X$ such that $\downarrow {\rm C}_F(X)$ is metrizable but $X$ is not first-countable. (English) |
| Keyword:
|
space of continuous maps |
| Keyword:
|
Fell topology |
| Keyword:
|
hyperspace |
| Keyword:
|
metrizable |
| Keyword:
|
hypograph |
| Keyword:
|
separable |
| Keyword:
|
first-countable |
| MSC:
|
54B20 |
| MSC:
|
54C35 |
| MSC:
|
54E45 |
| idZBL:
|
Zbl 1265.54093 |
| idMR:
|
MR3017261 |
| . |
| Date available:
|
2012-08-08T09:06:56Z |
| Last updated:
|
2014-07-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142891 |
| . |
| 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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| . |
