lower set - definitie. Wat is lower set
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Wat (wie) is lower set - definitie

A SUBSET OF A PARTIAL ORDER THAT INCLUDES ALL SUCCESSORS OF ITS ELEMENTS
Lower set; Down set; Down-set; Down-set lattice; Down set lattice; Downset lattice; Downward closed; Initial segment; Principal down set; Principal lower set; Principal down-set; Up-set; Upward closed set; Final segment; Upward closure; Downward closure; Downward closed set; Upper set and lower set; Upper and lower sets

lower set         
<mathematics> A finite non-empty downward closed subset of a partial order. (1999-03-17)
downward closed         
upward closure         

Wikipedia

Upper set

In mathematics, an upper set (also called an upward closed set, an upset, or an isotone set in X) of a partially ordered set ( X , ) {\displaystyle (X,\leq )} is a subset S X {\displaystyle S\subseteq X} with the following property: if s is in S and if x in X is larger than s (that is, if s < x {\displaystyle s<x} ), then x is in S. In other words, this means that any x element of X that is {\displaystyle \,\geq \,} to some element of S is necessarily also an element of S. The term lower set (also called a downward closed set, down set, decreasing set, initial segment, or semi-ideal) is defined similarly as being a subset S of X with the property that any element x of X that is {\displaystyle \,\leq \,} to some element of S is necessarily also an element of S.