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单词 RminimalElement
释义

R-minimal element


Let A be a set and R be a relation on A. Suppose that B is a subset of A. An element aB is said to be R-minimalPlanetmathPlanetmath in B if and only if there is no xB such that xRa. An R-minimal element in A is simply called R-minimal.

From this definition, it is evident that if A has an R-minimal element, then R is not reflexiveMathworldPlanetmathPlanetmath. However, the definition of R-minimality is sometimes adjusted slightly so as to allow reflexivity: aB is R-minimal (in B) iff the only xB such that xRa is when x=a.

Remark. Using the second definition, it is easy to see that when R is a partial orderMathworldPlanetmath, then an element a is R-minimal iff it is minimal.

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更新时间:2025/5/4 21:07:23