I will be at the Galway Colloquium at Leicester, UK, on Monday, August 1st, 2016. I will give an introduction to T_{0} topology and domain theory there, aimed mostly at students in mathematics.

I will try to illustrate some of the key concepts in the field by progressing through a proof of Dana S. Scott’s theorem (1972) that the injective T_{0} spaces are the continuous lattices. This will be an opportunity to touch various subjects: dcpos, the specialization ordering, Sierpiński space, retracts, Stone duality, sober spaces and sobrification, b-spaces and algebraic posets, c-spaces and continuous posets, notably.

Have a look at the slides! Note that there are several grayed areas, which hide some of the proofs. This is on purpose: I am expecting the attendees to find the missing arguments by themselves. If you plan to come to Leicester, you may try to think about them in advance. Otherwise, have fun and try to find the arguments by yourselves! Note that most of the material is scattered through the book, too…