Author: Urs Format: MarkdownItexa minimum entry, for the moment just so as have a place to record the fact that two smooth functions are smoothly homotopic as soon as they are (continuously) homotopic
(It sure feels like we must have recorded this somewhere already, but I couldn't find it...)
<a href="https://ncatlab.org/nlab/revision/smooth+homotopy/1">v1</a>, <a href="https://ncatlab.org/nlab/show/smooth+homotopy">current</a>
a minimum entry, for the moment just so as have a place to record the fact that two smooth functions are smoothly homotopic as soon as they are (continuously) homotopic
(It sure feels like we must have recorded this somewhere already, but I couldn’t find it…)
Author: Urs Format: MarkdownItexstarting [here](https://ncatlab.org/nlab/show/smooth+homotopy#SmoothRefinementOfContinuousHomotopyRelativeClosedSubset) I have added more details on the refinement of continuous homotopy to smooth homotopy, pointing to the relevant theorems in Lee's "Introduction to Smooth Manifolds"
<a href="https://ncatlab.org/nlab/revision/diff/smooth+homotopy/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/smooth+homotopy/2">v2</a>, <a href="https://ncatlab.org/nlab/show/smooth+homotopy">current</a>
starting here I have added more details on the refinement of continuous homotopy to smooth homotopy, pointing to the relevant theorems in Lee’s “Introduction to Smooth Manifolds”
Author: linuxmetel Format: MarkdownItexTo think of smooth homotopy, $f, g$ should be smooth (I also checked the refered PDF).
<a href="https://ncatlab.org/nlab/revision/diff/smooth+homotopy/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/smooth+homotopy/3">v3</a>, <a href="https://ncatlab.org/nlab/show/smooth+homotopy">current</a>
To think of smooth homotopy, should be smooth (I also checked the refered PDF).