Seifert van Kampen: proof and identification

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Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.

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

Explores the composition of applications in mathematics and the importance of understanding their properties.

Covers the compact-open topology, defining maps between spaces and discussing continuous maps and preimages in topology.

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Covers normed vector spaces, topology in R^n, and the principle of drawers as a demonstration method.

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Covers the approximation of functions in Sobolev spaces using smooth functions.