| Title:
|
A generalization of Steenrod’s approximation theorem (English) |
| Author:
|
Wockel, Christoph |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
45 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
95-104 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we aim for a generalization of the Steenrod Approximation Theorem from [16, Section 6.7], concerning a smoothing procedure for sections in smooth locally trivial bundles. The generalization is that we consider locally trivial smooth bundles with a possibly infinite-dimensional typical fibre. The main result states that a continuous section in a smooth locally trivial bundles can always be smoothed out in a very controlled way (in terms of the graph topology on spaces of continuous functions), preserving the section on regions where it is already smooth. (English) |
| Keyword:
|
infinite-dimensional manifold |
| Keyword:
|
infinite-dimensional smooth bundle |
| Keyword:
|
smoothing of continuous sections |
| Keyword:
|
density of smooth in continuous sections |
| Keyword:
|
topology on spaces of continuous functions |
| MSC:
|
57R10 |
| MSC:
|
57R12 |
| MSC:
|
58B05 |
| idZBL:
|
Zbl 1212.58005 |
| idMR:
|
MR2591666 |
| . |
| Date available:
|
2009-06-25T18:16:46Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128295 |
| . |
| Reference:
|
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| Reference:
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| . |
