# 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
- Preliminaries
- A few notions and results from Set Theory that will be used
in the rest of the course: well-orderings, ordinals, cardinals,
combinatorics, trees.
- Elementarity
- 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
aleph
_{omega+1}
- A well-chosen subspace of Rudin's Dowker space.

Here is an all-in-one file.

k.p.hart@ewi.tudelft.nl
Last modified: Tuesday 23-08-2005 at 13:29:11 (CEST)