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 …

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 …

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'.

Sep 7, 2024 · Topological Markov chains: how does this computation of 'entropy' work? Ask Question Asked 1 year, 5 months ago Modified 1 year, 5 months ago

Jan 15, 2021 · This question is concerned about the connection between the étale fundamental group $$\pi_1^ {\text {ét}} (X,x)$$ and the topological fundamental group $$\pi_1 (X (\mathbb {C}),x).$$ …

Jun 13, 2025 · Yes, this simplified version works. In this case, we say that the two metrics are equivalent. To see that it works, notice that it is equivalent to saying that that the identity mapping is …

Apr 22, 2025 · It is analogous to vector space (in this case topological space) and it's basis (basis for the existing topology). It's easy (?) to study properties of vector spaces in terms of its basic elements. …

Feb 1, 2026 · 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.

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.

Nov 22, 2024 · Question about topological index of L (G) Ask Question Asked 1 year, 3 months ago Modified 1 year, 3 months ago