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 …

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 …

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 …

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.

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 …

14 Here, $\mathbb {R}_l$ is the lower limit topology on $\mathbb {R}$ and $\mathbb {R}_K$ is the K-topology on $\mathbb {R}$. I understand the proof that these topologies are strictly finer …

I have come across to the following question : Let Tα T α be a family of topologies on X X . Show that there is a unique smallest topology on X X containing all the collections Tα T α , and a …

Jun 11, 2022 · Instead of a neighborhood, how would one define the basic open sets of these topologies? For completeness, what do the open balls look like in the operator norm topology? …

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

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