Concept

Separated sets

Related lectures (13)

Focuses on a criterion for separability in recollement, demonstrating iron properties and applications in various cases.

Surfaces: The Torus

Explores the definition of surfaces, focusing on the torus and its construction through various examples and morphic images.

Projective Spaces: Separation and Definitions

Covers separated spaces, saturation properties, and projective spaces, including the real projective plane and compactness.

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Spectrum of Hyperbolic Surfaces

Explores the spectrum of hyperbolic surfaces, discussing thin C-principle, grad, normalized functions, minimum volume, and embedding properties.

Properties of Limits

Covers the properties of limits and functions of multiple variables.

Stone-Weierstrass Theorem

Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.

Advanced Analysis II: Matrix Diagonalization

Covers matrix diagonalization, compact sets, continuity of functions, and the Mandelbrot set.

Base B for X: Connected Sets and Open Bases

Explores the concept of a base B for a topological space X and the properties of connected sets and open bases.

Sobolev Spaces in Higher Dimensions

Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.

Real Functions: Definitions and Theorems

Explores real functions, covering continuity, supremum, infimum, maximum, minimum, compact and connected sets, and the intermediate value theorem.

Advanced Analysis II: Eigenvalues and Compact Sets

Covers the reconstruction of a table using diagonal matrices and explores extreme values and set definitions.

Proper Actions and Quotients

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.