Continuity, Convergence, Cauchy’s sequences and examples
In this lesson, we will learn the continuity of a function, convergence of sequences and notion of Cauchy's sequence with examples and related results in metric spaces.
Course Material
- Metric Spaces (Definition & Examples)
- Some Further Examples of Metric Spaces
- Open Set, Closed Set, Neighborhood (with examples & results)
- Continuity, Convergence, Cauchy’s sequences and examples
- Completeness of Metric Space, Completeness Proofs
- Completeness Proofs
- Rare set, Bair’s Category Theorem
- Normed linear Spaces and Examples
- Mid Term Exam
- Finite dimensional normed spaces and Banach Spaces with Examples and results
- Quotient Spaces
- Continuous and bounded linear operators,
- Linear functional, examples and related results
- Linear operator and functional on finite dimensional Spaces.
- Inner product Spaces (definitions and examples)
- Hilbert Spaces (definitions and examples), Conjugate spaces,
- Representation of linear functional on Hilbert space, Reflexive spaces.
- Final Term Exam
- Chapters 18
- Department Mathematics
- Teacher
Dr. Azhar Hussain
