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.

Semester
2nd semester
Enrollment based on exam contract
Impossible
Grading method
Grading (scale from 0 to 20)
Can retake in second session
Yes
Enrollment Requirements
Registration for "Categorical Topology" is allowed if one has successfully accomplished "Advanced Topology".
Taught in
Dutch
Faculty
Faculty of Science and Bio-engineering Sciences
Department
Mathematics
Educational team
Robert LOWEN
Eva Colebunders (course titular)
Activities and contact hours

30 contact hours Lecture
30 contact hours Seminar, Exercises or Practicals
Course Content

(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.

Course material
Handbook (Recommended) : Abstract and Concrete categories, The Joy of Cats, J. Adamek, H. Herrlich G.Strecker, BIB, 9780486469348, 2009
Additional info

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 Outcomes

General competences

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.

Grading

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:

  • Other exam with a relative weight of 1 which comprises 100% of the final mark.

Additional info regarding evaluation

Oral exam and project evaluation

Allowed unsatisfactory mark
The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context

This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)