Stone-Weierstrass Theorem

Related lectures (28)

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Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers extreme values of continuous functions on compact sets and differentiability.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Explores dense sets, Cauchy sequences, periodic solutions, and unique solutions in differential equations.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores continuous functions on compact sets, discussing boundedness and extremum values.

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Explores the necessity of uniform continuity for continuous functions on compact sets.