Topic summary
Representing space
Extracted from the Wikipedia article Brown's representability theorem.
Statement of the theorem for CW complexes
Taking F(X) to be the singular cohomology group H(X,A) with coefficients in a given abelian group A, for fixed i > 0; then the representing space for F is the Eilenberg–MacLane spaceK(A, i). This gives a means of showing the existence of Eilenberg-MacLane spaces.