Author Archives: jgl

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 →

The book is out!  I’ve thanked several people at the beginning of the book, and I should now also thank everybody at Cambridge University Press, and notably Roger Astley, Helena Dowson, Clare Dennison, Caroline Mowatt, and Sarah Payne.  It was … Continue reading →

There are now two extra menus here. Let us skip the “course ideas” menu.  You see what I mean.  It might even be helpful. Instead, look at the “puzzles menu” if you’d like some relaxation.  All right, the intellectual kind: … Continue reading →

A model of a space X is a dcpo Y whose subspace of maximal elements is isomorphic to X. Of particular importance are those spaces that have ω-continuous models. This topic is covered in Section 7.7.2 of the book. Martin … Continue reading →

Polish spaces are an important class of spaces.  I am dealing with them in Section 7.7 of the book. But they are Hausdorff spaces, and the purpose of the book was to explore non-Hausdorff spaces. Matthew de Brecht found a non-Hausdorff … Continue reading →

This is all about “Non-Hausdorff Topology and Domain Theory – Selected Topics in Point-Set Topology“, a forthcoming book, to be published by Cambridge University Press. See the table of contents.