TITLE: finding an acyclic but not contractible space
QUESTION [6 upvotes]: I'm studying singular homology, and have come across the term acyclic.
I understood that a contractible space is acyclic, but can't find a counterexample showing the inverse is false.
Could anyone suggest me (hopefully the easiest) example?

REPLY [5 votes]: You can consider the exterior of the Alexander Horned Sphere. (see Hatcher-Algebraic Topology, p.169)