Author Archives: jgl

I hope you’ve had a Merry Christmas, and wish you a Happy New Year 2015.  To renew with an old habit, I’ve produced a new crosswords puzzle on the occasion (#14).  Sorry, it does not have anything particular related to … Continue reading →

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.