A Generalisation of Steenrod's Approximation Theorem
微分几何
2010-01-04 v1
摘要
In this paper we aim for a generalisation of the Steenrod Approximation Theorem from, concerning a smoothing procedure for sections in smooth locally trivial bundles. The generalisation 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
@article{arxiv.math/0610252,
title = {A Generalisation of Steenrod's Approximation Theorem},
author = {Christoph Wockel},
journal= {arXiv preprint arXiv:math/0610252},
year = {2010}
}