Connected Components

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Related lectures (28)

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Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Mayer-Vietoris Sequence

Explores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.

Graph Sketching: Connected Components

Covers graph sketching and connected components in streaming models.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Group Quotients and Push-outs

Explores group quotients and push-outs, discussing isomorphisms and surjectivity in different scenarios.

Whittaker Model: Properties and Analytic Continuation

Covers the properties of the Whittaker model and its analytic continuation.

Local Rings and Residues

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Local structure of totally disconnected locally compact groups III

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