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• 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