Hatcher-Algebraic-Topology · Problem 4.H.1

Homotopy Theory

Mathematics — Graph Theory · eckmann-hilton-duality

Problem

Show that if

A \hookrightarrow X

is a cofibration of compact Hausdorff spaces, then for any space

Y

, the map

Y^X \to Y^A

obtained by restriction of functions is a fibration. [If

A \hookrightarrow X

is a cofibration, so is

A \times Y \hookrightarrow X \times Y

for any space

Y