Jun 10, 2022 · I have been studying topological vector spaces, and despite going over numerous resources, the definitions of weak and weak-* topologies have been causing me some …

Sep 27, 2011 · The union of two topologies on some set may or may not be a topology. When is it a topology?

Aug 25, 2025 · I am reading some papers on operators acting on Banach spaces and one of them uses the following fact: If a vector space has two locally convex topologies with identical …

Nov 4, 2011 · In the case of topologies coming from norms on a vector space, two topologies are equivalent according to your definition if they are the same. For general topologies I find this …

Sep 7, 2019 · That are 3 more topologies (all homeomorphic to each other, if you already know that notion). One extra set that is a doubleton, so $\ {a,b\}$, $\ {a,c\}$ or $\ {b,c\}$, again three …

Apr 14, 2017 · There are a gazillion topologies on any infinite set and very few of these will be metrizable. Interesting non-metric topologies specific to $\Bbb {R}$, are the Sorgenfrey …

Feb 17, 2013 · Another Q is how many inequivalent topologies there are on a finite set. (Equivalent meaning homeomorphic.) I dk whether a formula for this has been found.

Jul 14, 2024 · Topologies on the space of smooth functions Ask Question Asked 1 year, 5 months ago Modified 1 year, 5 months ago

Oct 23, 2020 · The use I saw of this notion is of discussing the limit of spectra of operators, but I'm assuming there are plenty of uses which I don't suspect to look for. Can anyone please give …

May 2, 2021 · I am new to topology, and have been given an assignment to show that two topologies, on the same set, are the same (respectively). So far, in my class, we have only …