TACL school: course by Guram Bezhanishvili

Guram BezhanishviliTitle of the course: “Frames, topologies, and duality theory”

Course description: Frames are complete lattices that capture the basic features of topologies. The study of frames was initiated in the fifties of the last century. The resulting area is known as pointfree topology. The aim of this course is to present the basics of pointfree topology. The emphasis will be on providing pointfree descriptions of several well-known categories of topological spaces, such as compact Hausdorff spaces and Stone spaces, as well as their non-Hausdorff generalizations, spectral spaces and stably compact spaces. The corresponding categories of frames, as well as the resulting duality theory, will be discussed in detail. The celebrated Stone duality for Boolean algebras and for distributive lattices will be derived as corollaries. Applications of these results to logic will be mentioned towards the end of the course.

Slides lecture 1

Lecture 1 video

Slides lecture 2

Lecture 2 video

Slides lecture 3

Lecture 3 video

Slides lecture 4

Lecture 4 video