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Results tagged with manifolds
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user 8188
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.
24
votes
2
answers
3k
views
Are topological manifolds homotopy equivalent to smooth manifolds?
There exist topological manifolds which don't admit a smooth structure in dimensions > 3, but I haven't seen much discussion on homotopy type. …
- 825
58
votes
8
answers
9k
views
Is there a Whitney Embedding Theorem for non-smooth manifolds?
For smooth $n$-manifolds, we know that they can always be embedded in $\mathbb R^{2n}$ via a differentiable map. However, is there any corresponding theorem for the topological category? (i.e. …
- 825