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Results tagged with topological-manifolds
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A sufficient condition for a collection of open sets of a manifold to contain all open sets
Question
Let $k\geq 0$ be an integer and let $M$ be a topological $n$-manifold. Let $\mathcal{U}$ be a set of open sets of $M$ which satisfies the following closure properties:
(1). Let $U\subset M$ b …
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A sufficient condition for a collection of open sets of a manifold to contain all open sets
Yes, it is true that $\mathcal{U}$ contains all open sets of $M$. The proof is a minor modification of Weiss's argument, and proceeds in several steps.
Step1
We show that every open set of $M$ homeom …
- 2,292