Relatively compact subspace

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Related lectures (32)

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Convergence and Compactness in R^n

Explores adhesion, convergence, closed sets, compact subsets, and examples of subsets in R^n.

Cell Attachment: Gluing and Application

Covers cell attachment, gluing cells, and separability in a compact space.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Projective Spaces: Separation and Definitions

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

Joint Equidistribution of CM Points

Covers the joint equidistribution of CM points and the ergodic decomposition theorem in compact abelian groups.

Properties of X/G

Explores the properties of the quotient space X/G when X is compact and sometimes separated.

Introduction to Quantum Chaos

Covers the introduction to Quantum Chaos, classical chaos, sensitivity to initial conditions, ergodicity, and Lyapunov exponents.

Methods of Integration of Functions in Several Variables

Explores methods of integrating functions in several variables, emphasizing the importance of regular areas and changing variables to polar coordinates.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Open Subsets and Compact Sets

Discusses open subsets, compact sets, and methods for demonstrating openness in a space.