Hatcher-Algebraic-Topology · Problem 1.3.2

The Fundamental Group

Mathematics — Graph Theory · covering-spaces

Problem

Show that if

p_1 : \tilde{X}_1 \to X_1

and

p_2 : \tilde{X}_2 \to X_2

are covering spaces, so is their product

p_1 \times p_2 : \tilde{X}_1 \times \tilde{X}_2 \to X_1 \times X_2