| Title:
|
A non-archimedean Dugundji extension theorem (English) |
| Author:
|
Kąkol, Jerzy |
| Author:
|
Kubzdela, Albert |
| Author:
|
Śliwa, Wiesław |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
157-164 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove a non-archimedean Dugundji extension theorem for the spaces $C^{\ast }(X,\mathbb {K})$ of continuous bounded functions on an ultranormal space $X$ with values in a non-archimedean non-trivially valued complete field $\mathbb {K}$. Assuming that $\mathbb {K}$ is discretely valued and $Y$ is a closed subspace of $X$ we show that there exists an isometric linear extender $T\colon C^{\ast }(Y,\mathbb {K})\rightarrow C^{\ast }(X,\mathbb {K})$ if $X$ is collectionwise normal or $Y$ is Lindelöf or $\mathbb {K}$ is separable. We provide also a self contained proof of the known fact that any metrizable compact subspace $Y$ of an ultraregular space $X$ is a retract of $X$. (English) |
| Keyword:
|
Dugundji extension theorem |
| Keyword:
|
non-archimedean space |
| Keyword:
|
space of continuous functions |
| Keyword:
|
0-dimensional space |
| MSC:
|
46S10 |
| MSC:
|
54C35 |
| idZBL:
|
Zbl 1274.46131 |
| idMR:
|
MR3035503 |
| DOI:
|
10.1007/s10587-013-0010-8 |
| . |
| Date available:
|
2013-03-01T16:11:58Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143176 |
| . |
| 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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