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 …

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'.

"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 …

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 …

Sep 11, 2016 · For example, the topological dual (the space of all continuous linear functionals) of a Hilbert space is the Hilbert space itself, by the Riesz representation theorem, while the …

May 8, 2012 · A topological invariant is usually defined as a property preserved under homeomorphisms. There are topological properties, such as compactness 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 …

Feb 18, 2016 · Let X X be a set, so I want to prove that having the discrete topology is a topological property, but I am not sure how to do this since I know that every set can be made …

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 …

The linked book seems to be about something else, at least if you believe the description. It seems to be about computational aspects of topology, as opposed to using topological …