Instructor: Dr. Lajos SOUKUP
If you have any question, do not hesitate to write me
EMail:
soukup@renyi.hu or lsoukup@gmail.com
Gmail chat: lsoukup@gmail.com
Prerequisite:

set theory: operation on sets, cardinals, ordinals,
cardinal and ordinal arithmetic,
cofinalities, König lemma, transfinite induction, transfinite recursion,
Zorn lemma.
 topology: the notion of topological spaces, bases, metric spaces,
subspaces, continuous images, Cartesian products,
Books:
 Willard, Stephen; General topologyAddisonWesley, 1970
 Engelking, Ryszard General topologySigma series in pure mathematics ;
6. Heldermann Verlag, 1989.
 Juhász,I;Cardinal functions in topology  ten years later
(Mathematical centre tracts ; 123, 1980.
 Handbook of Set theoretic Topology
Course description
The goal of the course is twofold:
 we learn some basic notions and theorems of settheoretic and
general topology
 we practice the basic proof methods by solving problems
Grading: Course work 40%, Problem solving 40% Presentations 20%
A: 80100%, B: 6079%, C: 4059%, D: 3039%
Topics:

General Topology
 Axioms of separation
 Basic cardinal functions, weight, character and density, and related
inequalities
 Operation on topological spaces.
 Metric spaces and metrization theorems
 Compact and paracompact spaces
 Connected spaces
 Settheoretic topology
 Cardinal functions
 Combinatorial principles, Martin's Axiom, ♢,♣.
 Cardinal invariants of the reals,
 Selected problems:
 Dowker spaces
 Jakovlec spaces
 Scattered spaces
For more details see
Setop syllabus