Lebl-Basic-Analysis-I · Problem 7.6.10

Metric Spaces

Mathematics · fixed-point-theorem

Problem

Suppose

f: X \to X

is a contraction, and

(X,d)

is a metric space with the discrete metric, that is,

d(x,y) = 1

whenever

x \neq y

. Show that

f

is constant, that is, there exists a

c \in X

such that

f(x) = c

for all

x \in X