Means | Binary operations

Mean operation

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. (Wikipedia).

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From playlist Abstract Algebra

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Related pages

N-sphere | Idempotence | Topological space | Associative property | Commutative property | Semilattice | Euclidean space | Binary operation | Continuous function | Circle | Arithmetic mean | Algebraic topology