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 …

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 …

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

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 …

Here is Prob. 20 (a) in the book Topology by James R. Munkres, 2nd edition. Consider the product, uniform, and box topologies on $\\mathbb{R}^\\omega$. In which of these topologies are the following

13 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 than …

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 …

Jul 16, 2013 · Intersection of topologies Ask Question Asked 12 years, 4 months ago Modified 4 years, 11 months ago

If you show just one of: (i) there is a smallest topology containing all the T (ii) there is a largest topology contained in all the T, then the other statement can be seen as a corollary. It's a little easier to verify …