# Tagged Questions

In the mathematical field of topology, a uniform space is a set with a uniform structure. (Def: http://en.m.wikipedia.org/wiki/Uniform_space)

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I was reviewing questions and notes related to uniform spaces and came across this interesting statement: Every metric space is homeomorphic, as a topological space, to a complete uniform space. It ...
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### Topological groups are completely regular

I am studying topological groups, and I have been able to do quite a lot on my own by proving the propositions in this link on my own, but when I read up wikipedia that topological groups are all ...
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### When is a uniform space complete

From Wikipedia: a uniform space is called complete if every Cauchy filter converges. I was wondering if the following three are equivalent in a uniform space: every Cauchy filter converges, ...
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### The topology defined by the family of pseudo-distances.

A pseudometric (aka. pseudo-distance) is a metric except that maybe $x \neq y$ but $d(x,y) = 0$. Consider a family $(d_a)_{a \in A}$ of pseudometrics on a set $E$. For each $x \in E$ and each finite ...