# Eilenberg-Maclane space

From Topospaces

## Definition

Let be a group and an integer. If , we require that be Abelian. An **Eilenberg-Maclane space** for the pair denoted , is defined as a path-connected space whose homotopy group is , and for which all the other homotopy groups are trivial.

Eilenberg-Maclane spaces are unique upto weak homotopy-equivalence. In particular, among the class of CW-spaces, the Eilenberg-Maclane spaces are unique upto homotopy type.

In the particular case where the Eilenberg-Maclane space coincides with the classifying space for , viewed as a discrete group.