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 …

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 …

For any topological space X, the set of subsets of X with compact closure is a Bornology. If yes to 2, does it coincide with boundedness in a metric space and in a topological vector space? How is it …

"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'.

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? …

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.

Oct 15, 2023 · My book uses the abbrevation Top2 Top 2. I want to make sure I don't confuse it with the category Top × Top Top × Top. The topology Top2 Top 2 has arbitrary pairs of topological spaces as …

Jan 22, 2018 · What, intuitively, does it mean for a structure to be "topological"? I intuitively know what the set of vector spaces have in common, or the set of measure spaces.

Apr 21, 2024 · Another example is the cofinite topology on an infinite set. It is T1 T 1, hence every point is closed and there is no generic point. It is also irreducible (= hyperconnected) as any two nonempty …