In algebraic topology, a mean or mean operation on a topological space X is a continuous, commutative, idempotent binary operation on X.
If the operation is also associative, it defines a semilattice.
A classic problem is to determine which spaces admit a mean.
For example, Euclidean spaces admit a mean -- the usual average of two vectors -- but spheres of positive dimension do not, including the circle.
This topology-related article is a stub.