Mar 25, 2026 · What does it mean that points on a topological manifold are all equivalent? Ask Question Asked 4 days ago Modified 4 days ago

Apr 28, 2012 · A topological space is just a set with a topology defined on it. What 'a topology' is is a collection of subsets of your set which you have declared to be 'open'.

Feb 12, 2026 · Clearly all cofinal subnets are subnets using the inclusion map, but the converse is false. My query is, if we relax axioms 1-4 above to use cofinal subnets only, what would be the kind of …

Dec 6, 2025 · A topological space is locally connected if every point admits a neighbourhood basis consisting of open connected sets. To the definition given by Lee (Introduction to topological …

While in topological spaces the notion of a neighborhood is just an abstract concept which reflects somehow the properties a "neighborhood" should have, a metric space really have some notion of …

Mar 20, 2025 · Me and a friend has spend a lot of time recently pondering about topological spaces where every sequence is convergent, and we have made the following conjecture.

Topological dynamics is a subfield of the area of dynamical systems. The main focus is properties of dynamical systems that can be formulated using topological objects.

May 23, 2016 · Topological spaces can also be applied to settings where it's not clear how to define a metric, or even when you can't even apply the notion of metric space at all. An important example is …

Aug 5, 2022 · So with respect the last definition I am trying to prove that any topological group $ (X,*,\cal T)$ is completely regular using the following Munkres procedure.

Oct 6, 2020 · Please correct me if I am wrong: We need the general notion of metric spaces in order to cover convergence in $\\mathbb{R}^n$ and other spaces. But why do we need topological spaces? …