Oct 24, 2025 · the equivalence of two definitions of locally closed sets Ask Question Asked 11 years, 7 months ago Modified 1 month ago

Mar 22, 2021 · Let's say we want a general notion of " $ (X,\tau)$ is locally homeomorphic to $ (Y,\sigma)$." In general, $ (Y,\sigma)$ may not have the same "self-similarity" property of …

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

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 …

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?

Proving that a locally constant function is constant [duplicate] Ask Question Asked 5 years, 10 months ago Modified 5 years, 10 months ago

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

Oct 10, 2016 · 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 …

Nov 12, 2012 · Someone told me that locally compact Hausdorff spaces (unlike compact ones) need not be normal. Can one give me please such an example? Thank you.