Concept

Countably compact space

Related lectures (30)

Explores compact sets, extreme values, and function theorems on bounded sets.

Explains setting up experiments with compactness, isometries, and quasi-isometry.

Delves into renormalization, fractals, and strange attractors, exploring the properties of countable and uncountable sets.

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Covers the fundamental group of a reattachment and surjection proofs with neighborhoods and cover overlays.

Explores countable and uncountable sets, Cantor set, Mandelbrot set, and Box dimension in nonlinear dynamics and complex systems.

Covers strings, countable sets, cardinality, and the concept of countability, exploring the countability of various sets and Cantor diagonalization.

Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.

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

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

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

Explores the integrability of continuous functions on closed pavés and the properties of their integrals, including boundedness and Darboux sums.

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

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

Covers Morse theory, critical points, and Conley-Zehnder index in Hamiltonian systems.

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

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

Explores compact subsets of R^n, convergence theorems, and set properties.

Introduces measurable sets, functions, and the Cantor set properties, including ternary development of numbers.

Covers the description of all solutions of the initial problem and related concepts such as compactness and closure.