Dive into a comprehensive video series exploring the fundamental concepts of manifolds in mathematics. Begin with an introduction to topology and progress through key topics including interior, exterior, boundary, and closure. Examine Hausdorff spaces, quotient spaces, and projective space. Investigate second-countable spaces, continuity, and compactness. Explore locally Euclidean spaces and various examples of manifolds. Learn why projective space is considered a manifold. Conclude with an in-depth look at smooth structures, providing a thorough understanding of this essential mathematical concept.
Overview
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.
Taught by
The Bright Side of Mathematics
