Polish space

Related lectures (19)

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Covers the foundations of modern analysis, introductory functional analysis, and applications in MAB111.

Explores the implications of Baire Theorem in functional analysis and metric spaces.

Explores the Banach Fixed Point Theorem, showing the uniqueness of fixed points in contraction mappings.

Explores optimal transport regularity and Brenier's theorem, discussing continuity and convexity concepts.

Explores Hilbert space, scalar product, geometry, bases, complex functions, and quantum mechanics applications.

Covers the proof of Baire's Theorem, consequences of the Baire Category Theorem, and the principle of uniform boundedness.

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.

Explores the Fourier transform, Schwartz space, and Riemann-Lebesgue lemma in quantum physics.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.