- #1
Bleys
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So my teacher said that uniform continuity was a metric space notion, not a topological space one. At first it seemed obvious, since there is no "distance" function in general topological spaces. But then I remembered that you can generalize point-wise continuity in general topologies, so why not uniform continuity? I'm probably wrong; I wouldn't know the details to construct such a definition, but I know that Hausdorff spaces behave similarly to metric spaces (being Hausdorff themselves) in some respects, so maybe it would be possible?