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Results tagged with uniform-spaces
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user 21051
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Extensions of bounded uniformly continuous functions
$\DeclareMathOperator{\R}{\mathbb R}
\DeclareMathOperator{\eps}{\varepsilon}$
If you prefer to define uniformities in terms of a family $D$ of pseudometrics you can reduce the theorem to pseudometric …
- 11.4k
2
votes
Open mapping theorem for complete non-metrizable spaces?
Another example for question 2 is the following: There are linear partial differential operators with constant coefficients (e.g., the wave operator) and open sets $\Omega \subseteq \mathbb R^3$ (e.g. …
- 16.5k
1
vote
Complete uniform spaces require complete metrics?
Considering locally convex spaces as suggested by Peter Michor hints at typical counterexamples because the closed graph theorem usually forbids coarser Frechet space topologies. A concrete example is …
- 16.5k