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Tagged with compactification manifolds
6 questions
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Compact Manifold Realized as One-Point Compactification
I'm working on the following Problem from Lee's Introduction to Topological Manifolds:
"Let $M$ be a compact manifold of positive dimension, and let $p \in M$. Show that $M$ is homeomorphic to ...
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One-point compactification of $S^3\setminus S^1$ [closed]
Let $S^1$ be a circle embedded in $S^3$. Is the one-point compactification of $S^3\setminus S^1$ homeomorphic to $S^3$?
- 3,094
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Compactification of a noncompact regular level set of a map $\Bbb R^n\to \Bbb R$
Consider a smooth function $f:\Bbb R^n\to \Bbb R$, and a noncompact regular level subset $S=f^{-1}(c)$ for some regular value $c\in \Bbb R$. Then $S$ is a smooth hypersurface in $\Bbb R^n$, so it is ...
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Show every compact subspace of $m$-manifold has topological dimension at most $m$.
Notation $\bar{U}$ is the closure of $U$.
Definition $U$ is a neighborhood of $x$ means that $U$ is an open set containing $x$.
Definition An $m$-manifold is a Hausdorff space $X$ with a countable ...
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Thurston Compactification
Sorry in advance for my English.
I'm studying the Thurston compactification from the Jean-Pierre Otal's book "The Hyperbolization Theorem for Fibered 3-Manifolds".
I have a question, what $\mathbb{...
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Rational cohomology of section spaces of one point compactification of tangent bundles over closed manifolds.
Let M be a connected closed manifold ( oriented or nonoriented) of finite type (Betti numbers are finite) and $\Gamma(\mbox{TM}_{c})$ is the space of sections of fiberwise one point compactification ...
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