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2 votes
1 answer
198 views

A stronger version of paracompactness

Given a topological space $(X,\tau)$, recall that a cover $\mathcal{U}$ of $X$ is locally finite if for every point $x\in \mathcal{U}$ has a neighborhood $U$ that intersects finitely many elements of $...
11 votes
1 answer
441 views

Example of Banach spaces with non-unique uniform structures

While it is known that compact Hausdorff spaces admit unique uniform structures, it is further shown by Johson and Lindenstrauss's result that Banach spaces are characterized by their uniform ...