Manifolds

This course introduces manifolds through foundational topology, covering Hausdorff and quotient spaces, compactness, projective space, local Euclidean spaces, examples, and smooth structures.

Syllabus

Manifolds - Part 1 - Introduction and Topology.
Manifolds - Part 2 - Interior, Exterior, Boundary, Closure.
Manifolds - Part 3 - Hausdorff Spaces.
Manifolds - Part 4 - Quotient Spaces.
Manifolds - Part 5 - Projective Space.
Manifolds - Part 6 - Second-Countable Space.
Manifolds - Part 7 - Continuity.
Manifolds - Part 8 - Compactness.
Manifolds - Part 9 - Locally Euclidean Spaces.
Manifolds - Part 10 - Examples for Manifolds.
Manifolds - Part 11 - Projective Space is a Manifold.
Manifolds - Part 12 - Smooth Structures.