Category Archives: Uncategorized

Although I am trying to post about every month, I have not posted anything for two months.  My first idea was to talk about synthetic topology, after I read some papers by Weng Kin Ho and by Martín Hötzel Escardó. … Continue reading →

Both filter spaces and equilogical spaces form Cartesian-closed categories that contain Top as a full subcategory.  Is there any connection between them?  Very much so, as found by Reinhold Heckmann in 1998, following Martin Hyland (1977).  Read the full post.

A bit more than a month ago, I’ve been reminded of a beautiful construction of yet another Cartesian-closed category of spaces, generalizing the topological spaces: the equilogical spaces of Bauer, Birkedal, and Scott.  Simply put, equilogical spaces are formal (not … Continue reading →

As promised, let us talk about Wallman compactifications.  They extend the construction of the Stone-Čech compactification ßX, beyond discrete spaces, to all T4 spaces.  The construction is very similar to what we have seen in Filters IV.  But brace yourself … Continue reading →

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 →