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

Dec 24, 2023 · A locally $\kappa$ -presentable category is also locally $\lambda$ -presentable for any $\lambda>\kappa$. ¹ A regular cardinal is an infinite cardinal $\kappa$ with the property …

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 …

Is that correct or is there a counterexample (going either way)? The more important question is, what does locally trivial actually do for us? a. There is a trivial example of fibred manifold that …

Aug 19, 2020 · Locally closed subspace Ask Question Asked 5 years, 3 months ago Modified 5 years, 3 months ago

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 …

Jan 17, 2021 · My attempt so far seems to sort of blow by this, and I'm not confident it's correct - if it were true, it would seem that I can completely remove the regularity condition, which seems …

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 …

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