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Results tagged with uniform-spaces
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user 5903
4
votes
What can say about $2^X= \{A\subseteq X: A\text{ is closed set} \}$, when $(X, \mathcal{U})$...
As a first step you may want to work problem 8.5.16 in Engelking's General Topology. Keep in mind that a compact Hausdorff space has a unique uniformity, the sets of all neighbourhoods of the diagonal …
- 11.4k
1
vote
Accepted
A question about uniformities generated by pseudometrics
One direction:
let $\varepsilon>0$ and taken $N$ such that $\sum_{n>N}a_n<\frac12\varepsilon$. Take $\delta>0$ such that $\delta\cdot\sum_{n\le N}a_n<\frac12\varepsilon$. Now if $d_n(x,y)<\delta$ for …
- 11.4k
3
votes
Accepted
A a question about the metrization of uniform spaces
The relationship between the two pseudometrics is the following: $\rho(x,y)=2\cdot d(x,y)$ for all $x$ and $y$.
We compare the definitions of the pseudometrics in both books.
Both start with a sequenc …
- 11.4k
2
votes
Accepted
Chaos in uniform spaces
I believe the following works. Follow the proof in the reference supplied by Matthew Daws: choose two distinct periodic orbits and choose a compatible pseudometric $\rho$ such that all points in those …
- 11.4k
3
votes
A good place to read about uniform spaces
Why not try Weil's original paper: it's reference 12 in this paper.
- 11.4k