Jun 10, 2022 · 8 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 …

Two topologies are called equivalent if any non-empty open set of the first topology contains a non-empty open set of the second topology and, conversely, every non-empty open set of the second …

Sep 7, 2019 · The exact number of topologies on a set of size n n has no known closed formula, in fact, and is an old open problem. For more references see here or search for topologies on the main page …

Apr 28, 2012 · Defining a topology (e.g. the choice of open sets) means nothing but making precise some sense of separation. The most interesting and nice topologies are those in between the …

Here, Rl R l is the lower limit topology on R R and RK R K is the K-topology on R R. I understand the proof that these topologies are strictly finer than R R, but I am at a loss to begin how to show they …

I would like to know if there is like a magical formula to know how many topologies exist on a finite set For example for X = {a, b, c} X = {a, b, c} I found 29 29, but I dont know if there are more or how to …

Jul 14, 2024 · Topologies on the space of smooth functions Ask Question Asked 1 year, 6 months ago Modified 1 year, 5 months ago

There are a gazillion topologies on any infinite set and very few of these will be metrizable. Interesting non-metric topologies specific to R R, are the Sorgenfrey topology and the left and right order …

Oct 23, 2020 · Can anyone please give some examples of intersting Applications\uses of Hausdorff distance and such 'hyper'-topologies? Even with relation to simplifying other known mathametical …

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 …