- University of Ottawa
Monday, March 9, 2020
Fino al 27 marzo. Orario e luogo ancora da definire.
"Point-free topology" is the theory of "locales". They are a type of spaces, very similar to topological spaces, except that they might not have an underlying set of points. Locales that have enough points are the same as topological spaces, but some locales have no points and are completely new objects. We will see how many notions and constructions of ordinary topology carry over to locales. Later in the course I will talk about the internal logic of categories of sheaves, which provide an extremely powerful tool to work with locales. I will explain how these mysterious "spaces without points" are closely connected to 'forcing' in set theory, as well as the strong connection between the the theory of locales and intuitionistic mathematics. The course will start with a basic introduction to category theory, including limits and co-limits, epi and monomorphisms, adjoint functors and adjoint functor theorem, etc. The theory of locales will give many illustrations and interesting example of these concepts.