Ordered Locales

Abstract: Order and topology both abound in mathematics, often even together. Combined, they form the notion of an ordered topological space. How can this notion be suitably generalised to the theory of point-free topology? In this talk we will discuss one possibility, based on the so-called Egli-Milner relation. To keep the talk accessible, we start with an introduction to the definition of locales and describe their adjunction with topological spaces. After that, we show how this adjunction can be extended to certain categories of ordered spaces and the newly introduced ordered locales. To finish the talk we highlight some ongoing work. First, we describe how we are using these techniques to study aspects of relativity theory. In particular, we describe ingredients for a "causal boundary" construction, and show how "domains of dependence" can be recovered as a natural Grothendieck topology on ordered locales. Lastly, time permitting, we discuss an "internal" generalisation of ordered locales. (Based on joint work with Chris Heunen and Prakash Panangaden.)

game theorylogic in computer scienceprogramming languagescomputer science theorycategory theory

Audience: researchers in the topic

University of Birmingham theoretical computer science seminar

Series comments: Meeting ID: 818 7333 5084 ~ Password: 217