Title: Spaces which invert weak homotopy equivalences,
Abstract: It is well known that if $X$ is a CW-complex, then for every weak homotopy
equivalence $f:A\to B$, the map $f_*:[X,A]\to [X,B]$ induced in homotopy
classes is a bijection. For which spaces $X$ is $f^*:[B,X]\to [A,X]$ a
bijection for every weak equivalence $f$? This question was considered by J.
Strom and T. Goodwillie. In this note we prove that a non-empty space inverts
weak equivalences if and only if it is contractible.