Questions tagged [gn.general-topology]

The Gromov-Hausdorff metric makes the set of compact metric spaces into a metric space itself. I am wondering what some natural generalizations there are for arbitrary topological spaces. Namely, is ...

This is a follow-up to my previous question, which has a negative answer. Here is the most general version that I'm interested: Does there exist a Boolean algebra $A$, an infinite cardinal $\kappa$, ...

The following question is an attempt to revise this one into what I intended. Important revisions are shown in bold. Are there any known examples of a compact Riemannian manifold $M$ with (possibly ...

$\DeclareMathOperator\b{b}\newcommand\B{{\operatorname B}}$I wish to get help understanding the content of two theorems of [Iva] that seem mutually contradictory. First some context. Let $\b(\mathbb{R}...

Edit: as explained in my comment on alesia's answer, I mistakenly did not ask below the question I intended (due to my misguided efforts to simplify it). Thus, I revised and reposted my question here. ...

Let $\mathcal M_1(S)$ be the (compact, metrizable) space of probability Borel measures on the circle $S=\{z\in\mathbb C: |z|=1\}$ with its weak $*$ topology, so $\mu_n\to\mu$ if and only if $$ \int_S ...