Set Theoretic and General Topology STT

Instructor: Dr. Lajos SOUKUP

If you have any question, do not hesitate to write me

E-Mail: 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 topologyAddison-Wesley, 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 set-theoretic and general topology
• we practice the basic proof methods by solving problems

Grading: Course work 40%, Problem solving 40% Presentations 20%
A: 80-100%, B: 60-79%, C: 40-59%, D: 30-39%
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
• Set-theoretic 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