Topology: Compactness and Continuity

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Related lectures (31)

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Jordan Curve Theorem

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

Topology of Adeles

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Recognizing a Quotient

Discusses the recognition of a quotient in topology and the properties of the quotient topology.

Properties of Convergence: Sequences and Topology

Discusses the properties of sequences, convergence, and their relationship with topology and compactness.

Geometric Considerations in Rn

Covers the concept of intervals in Rn using geometric balls and defines open and closed sets, interior points, boundaries, closures, bounded domains, and compact sets.

Topologie: Attachment Applications

Covers exercises on attaching 1-cells to intervals in topology.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Open Mapping Theorem

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

Space Identification: SO(3)

Explores the identification of the space SO(3) and the topology of SS-space of R₃(R).

Topology: Course Notes 2021

Covers course notes on topology, discussing Stasheff Mérida, cost-savings, and representative points.