All Questions

Everyone knows the Heine-Borel theorem characterizing compact subsets of Euclidean space. For any $n \in \mathbb N$ a set $A \subseteq \mathbb R^n$ is compact just in case it is closed and bounded (in ...

Problem. Does there exist a ZFC-example of a countably compact Hausdorff paratopological group which is not a topological group? (The problem posed 27 May 2015 by Alexander Ravsky on page 9 of Volume ...

It is asserted in A Course in Metric Geometry by Burago, Burago, Ivanov that there can be no more than continuum of mutually nonisometric compact spaces How is this proven? Its clear that there ...

Over at the nForum, we've been discussing sequential compactness. The discussion led me to realise that I naively assumed that nets were simply Big Sequences, and that I could make a reasonable guess ...