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Results tagged with manifolds
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user 3634
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.
33
votes
Accepted
Is every real n-manifold isomorphic to a quotient of $\mathbb{R}^n$?
Hahn–Mazurkiewicz Theorem: Suppose $X$ is a nonempty Hausdorff topological space.
Then the following are equivalent:
there is a surjection $[0,1]\to X$,
$X$ is compact, connected, locally connect …
- 12.5k
32
votes
Accepted
Suspension of a topological space
It’s not true. The Poincare sphere $P$ is a manifold, and its suspension is not. But its double suspension is homeomorphic to $S^5$ by Cannon’s “Double Suspension Theorem”. I learned about this from …
- 12.5k