A Generalisation of Steenrod's Approximation Theorem

Details A Generalisation of Steenrod's Approximation Theorem A Generalisation of Steenrod's Approximation Theorem

2006-10-07

arxiv.org/abs/math/0610252v1

Arch. Math. (Brno) 45 (2) (2009) 95

Mathematics

Differential Geometry

Scientific paper

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.

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