Courses
Set-theoretic methods in General Topology
lecturer: K. P. Hart
location: Free University Amsterdam
period: fall semester 2001
time: mo 14:45 - 16:30
place: room S2.03
description:
The last decades have seen an increasing level of sophistication in
the application of set-theoretic tools in (general) topology; so much so
that a separate discipline has emerged: Set-theoretic topology. This course
will introduce the students to the tools and methods of set-theoretic topology.
We shall see applications of, among others, partition calculus, model
theory and pcf theory. Prototypical examples are:
-
Arkhangelskii's theorem on the cardinality of first-countable compact
spaces. This theorem can be proved in diverse and illustrative ways.
-
M. E. Rudin's example of a normal, not collectionwise Hausdorff, (one-dimensional)
simplicial complex. Here model-theoretic methods provide a clear picture
of the construction.
-
Kojman and Shelah's Dowker space of small cardinality that is constructed
using pcf theory. Pcf theory is a (relatively) new and exciting way of
looking at problems in cardinal arithmetic with surprising applications.
Prerequisites
Basic General Topology: separation and covering properties such as
normality and (para)compactness; compactifications; (ultra)filters;
connectedness.
Basic Set Theory: up to and including cardinal and ordinal numbers.
Literature
These papers give a good idea of what may be dealt with in the course:
-
Alan Dow. An introduction to applications of elementary submodels to topology.
Topology Proceedings 13 (1988), 17--72.
-
Alan Dow. Set theory in topology. Recent progress in general topology
(Prague, 1991), 167--197, North-Holland, Amsterdam, 1992.
-
Alan Dow. More set-theory for topologists. Topology and its Applications
64 (1995), 243--300.
- Webpage
of the course at the VU.
Activities
Free
University Topology Seminar
TU Delft Topology
Seminar
The two seminars will have joint bi-weekly sessions.
See the respective web pages for details.
Maintained by: K. P. Hart
Last modified: Thursday 22-07-2004 at 15:10:27 (CEST)
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