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.
Please email me (t.takahashi (at) uva.nl) for registration.
Tutorials, Q&A sessions, and group presentation will be in persion.
The group presentation should focus on a more advanced concept or idea that is related to topology and logic. Several suggested topics will be provided during the project, but students are also welcome (and encouraged) to explore their own topics based on their interests. Further details about the group presentation will be discussed during the tutorial Q&A sessions.