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Welcome to Functional Analysis Metric Spaces Introduction Topological proterties of Metric Spaces Functions in Metric Spaces Compact Metric Spaces Banach Fixed Point Theorem Hilbert Spaces: Inner Product Spaces Introduction Subspaces of Inner Product Spaces Orthogonal Bases and Fourier Series Dual of Hilbert Spaces Linear Operators in Hilbert Spaces Normed Vector Spaces Introduction Normed Vector Spaces Semi-normed Vector Spaces Examples of Normed Vector Spaces Vector Series: Schauder Bases Linear Operators Introduction Fundamental Theorems on Linear Operators Application to Invertible Operators Topological Dual of Vector Spaces Examples of Dual Spaces Weak Topologies More on Linear Operators Compact Operators-Part 1 Compact Operators-Part 2 Closed Operators Adjoint Operators-Part 1 Adjoint Operators-Part 2