Set-theoretic methods in Topology
This is a course that I gave at the Free University in the fall of 2001.
There is a separete PDF file for each chapter
Here is an all-in-one file.
- A few notions and results from Set Theory that will be used
in the rest of the course: well-orderings, ordinals, cardinals,
- 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
- A well-chosen subspace of Rudin's Dowker space.
Last modified: Tuesday 23-08-2005 at 13:29:11 (CEST)