Lebl-Basic-Analysis-I · Problem 7.6.6

Metric Spaces

Mathematics · fixed-point-theorem

Problem

a) Find an example of a contraction

f: X \to X

of a non-complete metric space

X

with no fixed point. b) Find a

1

-Lipschitz map

f: X \to X

of a complete metric space

X

with no fixed point.