Topology

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The aim of lecture is the systematization and deepening the knowledge of general topology.

Requirements:

Basic course of Calculus and Linear Algebra (in the extent of the courses 01MA, 01MAA2-4, 01LAP, 01LAA2 held at the FNSPE CTU in Prague).

Syllabus of lectures:

1.Structure on the set. 2. Real number and plane. 3.Sets, products and sums. 4. Graphs. 5. Mathematical structures. 6. Abstract spaces. 7. Structure of topological spases. 8. Separation axioms. 9. Hausdorff spaces. 10. Normal spaces. 11. Compact spaces. 12. Topology of metric. 13. Metric spaces.

Syllabus of tutorials:

Study Objective:

Knowledge : mathematical basis for a general topology. Skills: able to think in the schema definition, theorem and proof, and the use of general topology.

Study materials:

Key references: [1] John L. Kelly, (Springer, 1975, 315 pp., ISBN10:0-387-90125-6), [2] Bourbaki; Elements of Mathematics: General Topology, Addison-Wesley(1966).

Recommended references: [3] Willard, Stephen (2004). General Topology. Dover Publications. ISBN 0-486-43479-6. [4] Basener, William (2006). Topology and Its Applications (1st ed.).Wiley. ISBN 0-471-68755-3.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Aplikovaná algebra a analýza (elective course)
• Matematické inženýrství - Matematická fyzika (elective course)
• Matematické inženýrství - Matematické modelování (elective course)
• Mathematical Engineering - Mathematical Physics (elective course)