Speaker: Rafał Gruszczyński (Nicolaus Copernicus University)
Date and Time: Thursday, November 6th 2025, 16:30-18:00
Venue: ILLC Seminar Room F1.15, Science Park 107 and online.
Title: Partition Contact Algebras
Abstract. Boolean Contact Algebras (BCAs) are Boolean algebras expanded with a binary relation C. Under the intended interpretation, the elements of the domain are treated as regions of space, and C as the contact relation between regions. They were put forward as a version of point-free theories of topology, and for 25 years, have developed into a vibrant area of research on the intersection of logic and mathematics.
In my presentation I will talk about a particular BCAs that arise from partitions of the unity. Given such a partition, we may define a contact relation in the following way: regions x and y are in contact iff they both overlap the same cell of a partition. This subclass of the class of BCAs is called in the presentation Partition Contact Algebras (PCAs).
PCAs have a natural interpretation. If the partition is finite, we may think of it as a resolution, and of its elements as pixels. The contact relation may then be thought of as a kind of rough or approximate nearness of regions relativized to the coarseness of the resolution: the more pixels we have, the less regions are in contact with each other.
In my talk, I will focus on algebraic aspects of PCAs.
This is a joint work with Sergio Celani and Paula Menchón (Tandil, Argentina).