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Results tagged with uniform-spaces
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user 21051
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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
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. …
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Accepted
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 …
- 16.5k