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Concept

Locally compact space

Related lectures (32)

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

Explains setting up experiments with compactness, isometries, and quasi-isometry.

Focuses on a criterion for separability in recollement, demonstrating iron properties and applications in various cases.

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

Covers the fundamental group of a reattachment and surjection proofs with neighborhoods and cover overlays.

Explores the properties of the quotient space X/G when X is compact and sometimes separated.

Covers separated spaces, saturation properties, and projective spaces, including the real projective plane and compactness.

Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.

Explores the integrability of continuous functions on closed pavés and the properties of their integrals, including boundedness and Darboux sums.

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

Explores the exponential law for mapping spaces and the role of compactness in topological theory.

Covers cell attachment, gluing cells, and separability in a compact space.

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

Discusses separation conditions, graph, and saturations in equivalence relations on a space.

Discusses open subsets, compact sets, and methods for demonstrating openness in a space.

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.

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

Explores pointed mapping spaces, the exponential law, adjunction properties, and homotopic classes.

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

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.