In the Pro seminar Topology I  topics  complementary to the  course Topology I will be discussed. In particular, we will talk about:

— Nets: Moore-Smith convergence

— Locally compact spaces

— Paracompact spaces

— Countability axioms

— Baire’s category theorem

— Urysohn’s lemma

— Urysohn’s metrication theorem 

— Tietze’s extension theorem

— Tychonov’s theorem for infinite products

— Compact open topology

— Compactly generates spaces

— Weak Haussdorf spaces

— Noetherian spaces

— Topological manifolds

— Partition of unity and imbedding of manifold 

— Cantor set and Peano curves

— Topology of SO(3)

— Fiber bundles

— Simplicial sets

— Classification of compact surfaces

In order to successful participate in this course it is recommended for the students to have some basic knowledge in Topology. Appropriate and complete literature for each of the topics will be provided.