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单词 ProximityGeneratedByUniformity
释义

proximity generated by uniformity


Definition. Let X be a uniform space with uniformity 𝒰. The uniform proximity, or proximity generated by U, is a binary relationMathworldPlanetmath 𝛿 on the subsets of X, given by the formulaMathworldPlanetmathPlanetmath

A𝛿B    U𝒰:U(A×B).

Correctness of the above proximity is given by the below theorem:

Theorem. Proximity generated by a uniformity is a proximity. In other words, X is a proximity space with proximity 𝛿.

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