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 …

Apr 20, 2020 · 6 I'm getting very confused distinguishing the difference between a locally constant sheaf and a constant sheaf. $\textbf {Constant sheaf}$: Let M be a vector space.

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

Jan 17, 2025 · I am reading Daniel Huybrechts's The Geometry of moduli spaces of sheaves. In the introduction of chapter 5. He uses the following result: Proposition: Any saturated subsheaf …

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 …

A locally convex TVS is one that has a basis at the origin consisting of balanced absorbing convex sets. The reason for the emphasis on "convex" is that that's what distinguishes locally convex …