Concept

Glossary of topology

Related lectures (14)

Covers the concept of universal covering and its properties, including examples and monodromy action.

Covers quotients in abelian groups and the concept of free abelian groups, showing that every abelian group is isomorphic to a quotient of a free abelian group.

Fubini Generalized

Explores Fubini's theorem, extending integration to complex regions like closed unit balls.

Riemannian distance, geodesically convex sets

Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.

Manifolds: Charts and Compatibility

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Demonstration of Theorem on Compact Functions

Explores the demonstration of a theorem on compact functions and non-regular boundaries.

Untitled

Homomorphisms: Birational Maps and Affine Varieties

Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.

Quotient by a Relation

Covers the concept of quotient space by a relation and its applications.

Inverse Limits and Topologies

Explores inverse limits, profinite completions, and Hausdorff topologies in group theory and topology.

Dimensionality Reduction: PCA & t-SNE

Explores PCA and t-SNE for reducing dimensions and visualizing high-dimensional data effectively.

Bounding the Poisson bracket invariant on surfaces

Covers the concept of bounding the Poisson bracket invariant on surfaces, exploring joint work with A. Logunov and S. Tanny.

Universal Covering

Explores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.

Separable L^2 Spaces

Covers the concept of separable L^2 spaces, demonstrating properties and providing examples.