Algebraic Topology · Problem 13

The Fundamental Group — Allen Hatcher

Mathematics — Topology · deformation-retraction

Problem

Show that any two deformation retractions

r^0_t

and

r^1_t

of a space

X

onto a subspace

A

can be joined by a continuous family of deformation retractions

r^s_t

0 \leq s \leq 1

, of

X

onto

A

, where continuity means that the map

X \times I \times I \to X

sending

(x, s, t)

r^s_t(x)

is continuous.