# Topology/Banach Spaces

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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 ${\displaystyle L^{p}}$ spaces over ${\displaystyle \mathbb {R} ^{n}}$ are Banach spaces.

Proof (under construction)

## Exercises

(under construction)

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