Oct 24, 2025 · the equivalence of two definitions of locally closed sets Ask Question Asked 11 years, 9 months ago Modified 2 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 "pointwise …

The openness of path components of any open subset is equivalent to locally path connectedness of the space. But there do exist a simply connected space that is not locally connected.

Jan 5, 2020 · In this proof of the statement that proper maps to locally compact spaces are closed, the fact that compact subspaces of Hausdorff spaces are closed is used. However, is it true that locally …

Mar 8, 2020 · In dimension $>2$ there are lots of (locally) symmetric spaces that are not of constant curvature, so you'd best stick to surfaces.

Aug 19, 2020 · Locally closed subspace Ask Question Asked 5 years, 4 months ago Modified 5 years, 4 months ago

A function is called locally Lipschitz continuous if for every x in X there exists a neighborhood U of x such that f restricted to U is Lipschitz continuous. Equivalently, if X is a locally compact metric space, …

Jul 14, 2020 · Another case that works for Baire category theorem: locally countably compact regular space.

Feb 6, 2023 · Question 2: Is a Borel measure on a $\sigma$ -compact space locally finite? I've asked this question before here, and a counterexample to Question 2 is proposed, but the counterexample …

Jun 7, 2024 · In my book, when It comes to prove that the integral function Is continuos on an interval X, It shows that it's "locally Lipschitz" on X and, therefore, continuos. At a First read, I didn't