# Equivalences of smooth and continuous principal bundles with infinite-dimensional structure group

```@article{Muller2006EquivalencesOS,
title={Equivalences of smooth and continuous principal bundles with infinite-dimensional structure group},
author={Christophe Muller and Christoph Wockel},
year={2006},
volume={9}
}```
• Published 6 April 2006
• Mathematics
Let K be a Lie group, modeled on a locally convex space, and M a finite-dimensional paracompact manifold with corners. We show that each continuous principal K-bundle over M is continuously equivalent to a smooth one and that two smooth principal K-bundles over M which are continuously equivalent are also smoothly equivalent. In the concluding section, we relate our results to neighboring topics.
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Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves