Oct 24, 2025 · the equivalence of two definitions of locally closed sets Ask Question Asked 11 years, 8 months ago Modified 1 month ago

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 …

Jan 3, 2018 · Now is there any easy enough example of a connected space that fails to be locally connected at some point? One example adduced by Munkres is the so-called topologist's sine …

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 …

I can’t think of a counter example to this, but I’m having trouble proving it. My original strategy was to prove that a $\sigma$ -compact Polish space is locally compact. However, as the comments …

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 …

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

Dec 20, 2023 · So the cokernel of $f^\#$ is locally free of rank $1$ and the transition map on the intersection of the two affine lines is $t \mapsto 1/t$, which means that the module is $\mathcal …