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A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.

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When a support of an isotopy is disjoint from a subset

Let $M=\mathbb{R}$ and let $X=\{0\}$ (edit: I see that you want the manifold to be compact, you can take $[-10,10]$ or $\frac{\mathbb{R}}{20\mathbb{\mathbb{Z}}}$ instead of $\mathbb{R}$ in the example …
Saúl RM's user avatar
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14 votes
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Can a smooth manifold be realised as the image of a smooth function?

Riemannian Manifolds. An introduction to curvature. Springer, 1997. …
Saúl RM's user avatar
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