Modern Analysis

VIDEO LECTURES PRESENTED BY DR. MAU NAM NGUYEN

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Chapter 1: Fundamentals

1.1 . Topological Spaces

• • • Open Sets and Closed Sets in the Euclidean Space Rn

    • Topological Spaces: Definition and Examples

    • The finite complement topology

    • Metric Spaces: Definition and Examples

    • Metric Spaces: Open Balls and Closed Balls

    • Metric Spaces: Open Sets and Closed Sets

    • Topological Spaces: the Interior of a Set

    • Topological Spaces: the Closure of a Set

    • Basis for a Topology

    • Topology Generated by a Collection of Sets

    • Initial Topology Generated by a Family of Mappings

    • Continuity of Functions