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Results tagged with uniform-spaces
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user 5583
12
votes
2
answers
713
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Start with a topological group, take the meet of the two uniformities, and take the topology...
And what else can be said, if so?
(Original math.SE post)
In more detail: Say $(G,\mathscr{T})$ is a topological group. It has a left uniformity $\mathscr{L}$ and a right uniformity $\mathscr{R}$. …
- 2,585
8
votes
4
answers
3k
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Finite dimensional vector spaces over a complete but not-necessarily-valued field
I'm essentially reopening this old question of Ricky Demer which was never fully answered.
Essentially the original question: Suppose we have a topological field $F$ which is complete, Hausdorff, and …
- 2,585
4
votes
1
answer
339
views
Does the weak approximation theorem hold for general topological fields?
The weak approximation theorem states that given a field $F$ and nontrivial inequivalent absolute values $|\cdot|_1,\ldots,|\cdot|_n,$ and letting $F_i$ denote $F$ with the topology from $|\cdot|_i$, …
- 2,585
12
votes
0
answers
224
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Do compact inverse-property loops (or just compact Moufang loops) have invariant uniformitie...
So, the overall question is in the title: Does a compact topological loop with the inverse property have a Haar measure that is simultaneously left and right invariant? (And we can restrict to Moufan …
- 2,585