Oct 24, 2025 · the equivalence of two definitions of locally closed sets Ask Question Asked 11 years, 7 months ago Modified 26 days ago

Actually, a continuously differentiable function is locally Lipschitz, but since the derivative isn't assumed continuous in the theorem, one has only the weaker property that might be dubbed …

Aug 19, 2020 · Locally closed subspace Ask Question Asked 5 years, 3 months ago Modified 5 years, 3 months ago

Jun 2, 2020 · My intuition suggests that a continuously differentiable function on a convex set which is locally convex everywhere should be globally convex, but I have trouble constructing …

So any incomplete locally compact metric space is a counter-example to "only if". Moreover, as mentioned Tsemo Aristide's answer, any non-compact metric space, even a proper one, has …

Apr 4, 2019 · But this work in exactly the opposite direction then the problem we have here. Does anybody see how the auther here conclude that $\Delta_X$ is locally closed immersion?

The logic here is we would like to show the gradient of a $C^1$-function is locally bounded on a locally compact space, thus to obtain the Lipschitz continuity.

I am trying to show that a function that is locally constant on a connected space is, in fact, constant. I have looked at this related question but my approach is a little different than the …

Jul 18, 2022 · There are different definitions for topological manifolds, sometimes second-countability or paracompactness are added to being locally euclidian Hausdorff. (Sometimes …

Oct 24, 2014 · I need to show that: If $X$ is locally compact, second countable and Hausdorff, then $X^*$ is metrizable and hence $X$ is metrizable. I have already showed that every …