Basic Analysis I — Real Analysis · Problem 7.4.7

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · completeness-and-compactness

Problem

Let

C\bigl([a,b],\mathbb{R}\bigr)

be the metric space as in Example 7.1.8. Show that

C\bigl([a,b],\mathbb{R}\bigr)

is a complete metric space.