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Functional Analysis

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1.Theorem: Nested Closed Subset Theorem

2.Banach Spaces and Banach Algebra

3.Hilbert Spaces

4.Linear Operators and Linear Functionals

5.Non-linear Operator

6.Lebesque Measure and Lebesque Integral

7.Simple Connectivity

8.The $C(X)$ Algebra

9.Compact Sets

10.Definition: Sigma-Algebra

11.Definition: Ring of Sets (measure-theoretic definition)

12.Definition: Functional

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