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. I soon realized I would have trouble to match the level of clarity they reach in their papers. Let me recommend [1], or [2] if you’ve got more time. Maybe I’ll talk about these one day, who knows.

In the meantime, I realized I’ve never talked about any of my research. Last year, Achim Jung and myself found a nifty theorem, one of those theorems in mathematics that states that several, apparently unrelated notions are in fact the same. Jimmie Lawson and Xiaoyong Xi found the same result independently. This all builds on the related notions of locally finitary compact spaces, and of quasi-continuous dcpos, and I’ll start to introduce you to the latter. See the full post.

[1] Martín Hötzel Escardó and Weng Kin Ho. *An operational domain theory and topology of a sequential programming language.* Information and Computation 207(3), p. 411-437, Elsevier, 2009.

[2] Martín Hötzel Escardó. Synthetic topology of data types and classical spaces. ENTCS, Elsevier, volume 87, pages 21-156, November 2004.