Set-theoretic methods in Topology

This is a course that I gave at the Free University in the fall of 2001.

Lecture Notes

There is a separete PDF file for each chapter
A few notions and results from Set Theory that will be used in the rest of the course: well-orderings, ordinals, cardinals, combinatorics, trees.
An introduction to the use of elementary substructures of the universe in set theory and topology.
Arkhangelskii's theorem
Arkhangelskii's theorem on the cardinality of first-countable spaces is a very good example of elementarity at work. We present Arkhangelskii's own proof, the Pol-Sapirovskii argument and the elementary version of the latter.
Dowker spaces
The rest of the notes will be devoted to Dowker spaces. This is a quick introduction to the subject.
Balogh's Dowker space
This Dowker space uses the machinery of elementary substructures in its construction.
Rudin's Dowker space
The first real Dowker space.
A Dowker space of size alephomega+1
A well-chosen subspace of Rudin's Dowker space.
Here is an all-in-one file.
Last modified: Tuesday 23-08-2005 at 13:29:11 (CEST)