6 ECTS credits
150 h study time
Offer 1 with catalog number 4013394FNR for all students in the 2nd semester at a (F) Master - specialised level.
(1) Topological constructs
Topological categories. Special morphisms. Limits and colimits. Factorizationsystems for morphisms.
Reflective and coreflective subconstructs, Stability of constructions. Relation with completion and compactification theories.
(2) Exponential objects and Cartesian closedness
Existence of function spaces, relation to compatibility of constructions. Situation in TOP. Characterisation of exponential objects in TOP.
(3) Extensional topological constructs and topological universes
(4) Examples
Limit spaces and pseudotopological spaces and function space of continuous convergence
Topological subconstructs of TOP, Sequential spaces and Compactly generated spaces. Cartesian closedness
Uniform spaces characterised by covers and generalisation to coverring spaces. Embedding of TOPs and of paracompact spaces.
Study Material
Course notes are given to the students, based on the following material:
Additional Study Material
(1) J. Adamek, H. Herrlich G.Strecker: Abstract and Concrete categories, Wiley, 1990
Learning Aims
The contents are related to the research carried out in the research group. Basic preparation to research topics in Categorical Topology is part of the course. It is expected from the student that, using the course notes, proofs can be worked out in detail and that exercises can be solved.
The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.
Within the Other Exam category, the following assignments need to be completed:
Oral exam and project evaluation
This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)