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 confusion. I …

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

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 extra …

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

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 topology and …

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 some …

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 discussed metric …

Everything involving general topological spaces: generation and description of topologies; open and closed sets, neighborhoods; interior, closure; connectedness ...

Oct 12, 2013 · I am trying to solve the following problem: In which topologies (uniform, product, box) are the following functions from $\mathbb {R}$ to $\mathbb {R^\omega}$ continuous?