A generalization of Steenrod’s approximation theorem

Christoph Wockel

Archivum Mathematicum (2009)

  • Volume: 045, Issue: 2, page 95-104
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Wockel, Christoph. "A generalization of Steenrod’s approximation theorem." Archivum Mathematicum 045.2 (2009): 95-104. <http://eudml.org/doc/250554>.

@article{Wockel2009,
abstract = {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.},
author = {Wockel, Christoph},
journal = {Archivum Mathematicum},
keywords = {infinite-dimensional manifold; infinite-dimensional smooth bundle; smoothing of continuous sections; density of smooth in continuous sections; topology on spaces of continuous functions; infinite-dimensional manifold; infinite-dimensional smooth bundle; smoothing; continuous sections; density; space of continuous functions},
language = {eng},
number = {2},
pages = {95-104},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A generalization of Steenrod’s approximation theorem},
url = {http://eudml.org/doc/250554},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Wockel, Christoph
TI - A generalization of Steenrod’s approximation theorem
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 2
SP - 95
EP - 104
AB - 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.
LA - eng
KW - infinite-dimensional manifold; infinite-dimensional smooth bundle; smoothing of continuous sections; density of smooth in continuous sections; topology on spaces of continuous functions; infinite-dimensional manifold; infinite-dimensional smooth bundle; smoothing; continuous sections; density; space of continuous functions
UR - http://eudml.org/doc/250554
ER -

References

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