Category Archives: Uncategorized

While we’ve got a good theme, let’s hang on to it.  Yes, of course: filters.  It turns out that you can build compactifications using ultrafilters, in special cases.  See the full post.  I’ll talk about more general constructions later.

Not that I’m particulary Irish, but here’s a crossword puzzle for Saint Patrick’s Day.  (Also playable online.)  Meant to be the shape of a cloverleaf… Don’t omit the other 12 puzzles, too.

While listening to some talks at the special session on categorical topology last Saturday, I realized that I had said something wrong at the end of part II: the filter spaces satisfying the property that any intersection of filters that … Continue reading →

I’m currently at the Joint Mathematics Meeting in Baltimore, MD, USA.  This is a huge conference.  The program alone is a 250+ page booklet! My main purpose there is to participate in the special session on categorical topology on Saturday, … Continue reading →

The Christmas 2013 puzzle is out!  (also playable online.)  Note the black squares make a kind of Christmas cracker shape… Don’t omit the other 11 puzzles, too.

I said earlier that what convergence was the starting point of topology.  Why not take this seriously and replace topological spaces by spaces that would be defined in terms of notions of convergence directly, instead of through opens? One bonus … Continue reading →

It’s out!  And freaky difficult as well…  Play it online, too, and don’t forget the other topology-related crossword puzzles.  Enjoy!

It’s been a long time, and I haven’t given any news from the Summer Topology Conference. There I met Frédéric Mynard. Frédéric stressed the importance of filters to me, and I should mention a few of the nice things one … Continue reading →

I’m off to the Summer Topology Conference, North Bay, Ontario, Canada.  I’ll be giving two talks there.  One is directly related to Chapter 7 of the book, and may help get a global vision of what’s going on there: have … Continue reading →

Dito Pataraia once came up with an elegant proof of (essentially) the Bourbaki-Witt theorem.  The proof is very short, and deserves a look.  Furthermore, it uses domain theory in an essential way: the core is showing that the set of … Continue reading →