1st Semester 2025/26: Topology in and via Logic
- Instructors
- Tenyo Takahashi, Nick Bezhanishvili
- ECTS
- 6
- Description
Topology is one of the basic areas of contemporary mathematics, and plays a significant role in many areas of logic: from mathematical subjects (model theory, set theory, category theory, algebraic logic) to areas of philosophy (epistemic logic, formal epistemology), as well as formal semantics and theoretical computer science (domain theory, learning theory). The key idea behind topology is that spaces can be understood through simple building blocks – so-called “open” and “closed” sets – and their interactions. This framework captures not only the intuitive features of physical space but also a wide variety of abstract notions of “spaces,” such as spaces of ideals, information spaces, and spaces of actions.
This project introduces students to the concepts of topology as they are used in logical practice. It combines a series of introductory lecture recordings covering the basic concepts commonly used in the logical setting (continuity, neighbourhood filters, compactness, connectedness, separation) with Q&A sessions that focus on practical applications and help students select appropriate presentation topics. Students will also have the opportunity to explore more advanced topics according to their interests. Throughout the project, we will emphasize how topology appears naturally in many logical contexts.
- Organisation
6 lecture recordings + 1 Tutorial + 2 Q&A sessions + Group presentation
Week 1: A brief kick-off meeting + 3 lecture recordings + Tutorial
Week 2: 3 lecture recordings + Q&A
Week 3: Q&A + Group consultations
Week 4: Group presentations
- Prerequisites
Mathematical maturity.
- Assessment
3 Homework assignments + Group presentation
- References
There are lecture notes and slides available.
Other references include:
Ryszard Engelking (1968). General Topology.
Steven Vickers (1996). Topology via Logic.
Jorge Picado, Aleš Pultr (2012). Frames and Locales: Topology without Points.
Tai-Danae Bradley, Tyler Bryson, and John Terilla (2020). Topology: A Categorical Approach.
More specific references will be made available during the project.