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Results tagged with manifolds
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user 32487
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.
4
votes
1
answer
439
views
Is a manifold-with-boundary with given interior and non-empty boundary essentially unique?
Let $M$ be a compact connected manifold-with-boundary such that $\circ M \neq \emptyset$, where $\circ M$ is the boundary of $M$. Let $N$ be a compact connected manifold-with-boundary such that $\circ …
- 397
7
votes
1
answer
406
views
When is a manifold boundary a deformation retract of its open neighborhood?
Clearly $\partial M$ being collared in $M$ is a fairly general sufficient condition (this includes paracompact manifolds). …
- 397
5
votes
2
answers
551
views
Collared boundary of a non-metrizable manifold
Every metrizable manifold-with-boundary has a collared boundary, as shown in "Locally flat imbeddings of topological manifolds", Morton Brown, 1962. …
- 397
1
vote
Collared boundary of a non-metrizable manifold
The following strengthening of the theorem in Gauld's book "Non-metrizable manifolds" holds:
Let $X$ be a manifold-with-boundary. … Applied to manifolds-with-boundary, if $X$ is a manifold-with-boundary, $Y$ is a (boundaryless) manifold, and $\partial X$ is $X$-collared, then $X \times Y$ is a manifold-with-boundary, and $\partial …
- 397