Topology/Banach Spaces

A Banach space is a normed vector space that is complete with respect to the inferred metric.

Examples

Recalling that a space is complete if all Cauchy sequences converge. Then $L^{p}$ spaces over $\mathbb {R} ^{n}$ are Banach spaces.

Proof (under construction)

(under construction)

This article is issued from Wikibooks. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.