Syllabus
1. Category, functor, natural transformation.
2. Diagrams, limits and colimits.
3. The Maranda Theorem and existence of colimits.
4. Yoneda lemma.
5. Adjoint functors.
6. Abelian categories.
7. Topological spaces and continuous maps.
8. Separation axioms, Hausdorff, regular and normal spaces.
9. Compact spaces; the Tichonov and Baier Theorems, Cech-Stone compactification.
10. Uniform spaces.
Annotation
An introductory course in category theory and general topology.
A recommended course for specialization Mathematical Structures within General Mathematics.