Let X be a connected CW complex and let
K(G,n) be an Eilenberg-Mac Lane CW complex where
G is abelian. As K(G,n) may be taken to be
an abelian monoid, the weak homotopy type of the space of
continuous functions X → K(G,n)
depends only upon the homology groups of X. The purpose of this
note is to prove that this is true for the actual homotopy
type. Precisely, the space map∗(X,
K(G,n)) of pointed continuous maps X
→ K(G,n) is shown to be homotopy equivalent
to the Cartesian product
Homology, Homotopy and Applications, Vol. 15 (2013), No. 1, pp.137-149.
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