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Results tagged with uniform-spaces
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user 26013
3
votes
Accepted
Extending uniformly continuous functions on subspaces to non-metrizable compactifications
The closure of $X$ in $Z$ is compact , so there is no hope if $f$ is not bounded. If it is bounded then so is its extension to the closure of $X$ in $Y$ and this gives a bounded uniformly continuous …
- 2,409
2
votes
Accepted
Tensor product of C*-algebras of bounded, uniformly continuous functions on metric spaces
The spectrum of the $C^\ast$-algebra of bounded, uniformly continuous functions on a uniform space is the Samuel compactification. So your query can be restated in the form:
is the Samuel compactific …
- 2,409
1
vote
Uniformities generated by metrics.
From your remarks one can see that the core of your question lies in the case of a product of metric spaces. But a large cardinal product, say of the real line, cannot have a structure generated by m …
- 2,409