Zulip Chat Archive

I gave a talk at CMU about LTE, and someone in the audience asked about the idea/intuition behind the terminology "condensed sets". Why "condensed"? I didn't have a very good answer to this. @Peter Scholze do you explain this somewhere?

Adam Topaz (Mar 02 2021 at 15:57):

If extremally disconnected sets are "clouds of dust" then a condensed set is a condensed cloud of dust?

Peter Scholze (Mar 02 2021 at 15:57):

Something like this

Peter Scholze (Mar 02 2021 at 15:57):

I mean sets are just isolated points in free space. A condensed set has taken some form

Peter Scholze (Mar 02 2021 at 15:57):

like an interval, or a Cantor set, ...

Peter Scholze (Mar 02 2021 at 15:58):

We were looking for some word that expresses the idea that these points are somehow bound together

Johan Commelin (Mar 02 2021 at 15:59):

Ok, thanks. During the discussion in CMU the cantor set was also mentioned as somehow a condensed bunch of points. So I guess we sort of figured out the right reason

Peter Scholze (Mar 02 2021 at 15:59):

(In German, the correct translation is by the way "verdichtet", not "kondensiert" (which would be what water does at a window when it's cold outside).)