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

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 …

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 …

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 …

Apr 20, 2020 · 7 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.

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 …

May 9, 2021 · Henno Brandsma’s answer tells us that in fact pointwise countable partitions give rise to locally finite ones. That’s quite cool and relevant, but my question really is about asking …

Apr 4, 2019 · But this work in exactly the opposite direction then the problem we have here. Does anybody see how the auther here conclude that $\Delta_X$ is locally closed immersion?

Jun 19, 2020 · Sorry for my lack of extract. In ,III. Proposition 6.5 , Hartshorne named loacally free of finite rank resolution "locally free resolution".