Algebraic Topology · Problem 4K.2

Homotopy Theory — Allen Hatcher

Mathematics — Topology · dold-thom-theorem

Problem

Show that a simplicial map

f: K \to L

is a homotopy equivalence if

f^{-1}(x)

is contractible for all

x \in L

. [Consider the cover of

L

by open stars of simplices and the cover of

K

by the preimages of these open stars.]