Oct 24, 2025 · the equivalence of two definitions of locally closed sets Ask Question Asked 11 years, 7 months ago Modified 13 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 …

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

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 …

Aug 19, 2020 · Locally closed subspace Ask Question Asked 5 years, 2 months ago Modified 5 years, 2 months ago

Aug 23, 2018 · Does this answer your question: In $\Bbb R^n$ , locally Lipschitz on compact set implies Lipschitz?

Jun 19, 2020 · locally free resolution of coherent sheaf on quasi-projective scheme Ask Question Asked 5 years, 4 months ago Modified 3 months ago

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 …

May 5, 2025 · Note that local conformal flatness is a property of Riemannian manifold, so you need to specify a Riemannian metric. Amazingly, every 2-dimensional Riemannian manifold is …