Normed Spaces: Definitions and Examples

Related lectures (27)

Page 2 of 3

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Covers norms, convergence, sequences, and topology in Rn with examples and illustrations.

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Explains the definition of Sobolew spaces and their main properties, focusing on weak denivelre.

Introduces key concepts in numerical analysis and optimization, focusing on distances, subsets, and their properties in R^n.

Covers a recap of Analysis 1 and 2, emphasizing normed space R^n, subsets, and continuous functions.

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

Covers the standard properties of distance and norm in vector spaces.

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

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