First and second countable spaces: Definitions, examples and related results
Lipschutz, S., General Topology, latest edition, (Schaum’s outline series. NY:McGraw Hill).
Chapter No. 9
Course Material
- Topological spaces: Introduction, Definition & Examples
- Limit Point, Interior Point, Closure, exterior and boundary of set: Definitions, Examples and related results
- Convergent sequences, Relative topology: Definitions, examples and related results
- Bases and sub-bases: Definitions, examples and related results
- Local bases, Continuous functions: Definitions, examples and related results
- Continuity and sequentially continuity at a point, Open and closed functions
- Homeomorphism: Definition, examples and related results
- First and second countable spaces: Definitions, examples and related results
- Mid Term Exam
- Lindelof's Theorems, separability
- Separation axioms: T_0. T_1 and T_2 spaces
- Regular and normal spaces: Definitions, examples and related results
- Functions that separate points, Completely regular spaces, Tychonoff spaces
- Compact sets: Definition, examples and related results
- Subsets of compact spaces, sequentially compact sets
- Product spaces: Definition, examples and related results
- Connectedness: Definition, examples and related results
- Final Term Exam
- Chapters 18
- Department Mathematics
- Teacher
Dr. Azhar Hussain
