Feb 6, 2026 · What is the relation between the four variants? The Wikipedia variant is a stronger requirement than Hatcher's. Locally simply connected spaces are semilocally simply connected and …

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, 2019 · Why is the topological sum a thing worth considering? There are many possible answers, but one of them is that the topological sum is the coproduct in the category of topological spaces and …

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 …

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? …

"A topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms. That is, a property of spaces is a topological property if whenever a space …

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 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.

Sep 22, 2025 · B) If we want to define a measure directly on a topological space, the summation of an uncountable number of non-negative real numbers will become a difficulty. But I feel that my …

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.