A GENERALIZATION OF STEENROD'S APPROXIMATION THEOREM

被引：0

作者：

Wockel, Christoph ^{[1
]}

机构：

[1] Tech Univ Darmstadt, Fachbereich Math, Schlossgartenstr 7, D-64289 Darmstadt, Germany

来源：

ARCHIVUM MATHEMATICUM | 2009年 / 45卷 / 02期

关键词：

infinite-dimensional manifold; infinite-dimensional smooth bundle; smoothing of continuous sections; density of smooth in continuous sections; topology on spaces of continuous functions;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：95 / 104

页数：10

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