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About: Mean operation     Goto   Sponge   NotDistinct   Permalink

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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.