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Results tagged with uniform-spaces
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user 8628
2
votes
In the category of uniform spaces, is the completion of a quotient map also a quotient map?
I think the answer to the question is yes, but there is a little gap (called "Gap-Statement" below) that needs to be filled - and of course there is still the possibility that the "Gap-Statement" is f …
- 48.9k
1
vote
Accepted
The separated uniform space associated with $(X,\mathfrak{U})$
Let $(X,{\frak U})$ be a uniform space. We set $R = \bigcap {\frak U}$. It is a standard exercise to show that $R$ is an equivalence relation.
So we look at the following set:
$${\frak U}/R := \{A\su …
- 48.9k
1
vote
Construct a specific base for Fine uniformities in the diagonal(Entourages) case
Given a uniformity $\cal U$ on a set $X$, let $\tau_{\cal U}$ be the topology generated by (or compatible with) $\cal U$.
Let $\text{Uni}(\tau_{\cal U})$ denote the collection of uniformities compat …
- 48.9k