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

Oct 31, 2025 · The local citation to Hausdorff in the first lemma seems to be the difficult bit, so I will look into that one. I have seen a more compact - no pun intended - argument than the …

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 …

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

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 …

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

A condition on the function might be missing. Otherwise, in dimension 1, the function "fractional part" is locally injective but not injective on R.