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Results tagged with uniform-spaces
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user 6101
3
votes
Using the Stone-Weierstrass theorem to solve an integral limit
I understand the aim is an elementary proof; here is one.
Let $\omega$ be a modulus of continuity for $f$ on $[0,c]$. Then, for all $0<t\le c-1$
$$\int_0^1|f(x+t)-f(x)|^2dx\le \omega(t)\int_0^1\big(f( …
- 60.6k
6
votes
A good place to read about uniform spaces
How do they arise &c: metrization theorems are certainly a natural source. Under this point of view, the "uniformization" of a topology may be seen as a first main step towards metrization. Furthermor …
- 60.6k