empty set

(redirected from Nonempty set)
Also found in: Encyclopedia.

empty set

Mathematics
The set that has no members or elements.
The American Heritage® Student Science Dictionary, Second Edition. Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.
References in periodicals archive ?
If X is a nonempty set, [gamma] [member of] [Gamma] (X) and k [member of] [Omega], a subset A of X is said to be a [[disjunction].sub.k]-set if A = [[disjunction].sub.k](A) and A is said to be a [[conjunction].sub.k]-set if A = [[conjunction].sub.k](A).
For a nonempty set H a function [omicron] : H x H [right arrow] P*(H) is called a hyper operation on H.
Let X be any nonempty set. An element x [member of] X is said to be a fixed point of a multi-valued mapping T: X [right arrow] [2.sup.X] if x [member of] Tx, where [2.sup.X] denotes the collection of all nonempty subsets of X.
Let X be a nonempty set (decision space) and denote by [??] a preorder (i.e., a reflexive and transitive binary relation) on X.
Let X be a nonempty set and s [greater than or equal to] 1 be a given real number.
Let H be a nonempty set. Then the map [omicron] : H x H [right arrow] [P.sup.*](H) is called hyperoperation or join operation on the set H, where [P.sup.*](H) = P(H)\{0} denotes the set of all nonempty subsets of H.
Let E be a topological space, D a nonempty set, <D> the set of all nonempty finite subsets of D, and [GAMMA] : <D> [??] E a multimap with nonempty values [[GAMMA].sub.A] := [GAMMA](A) for A [member of] (D).
Graph G consists of a finite nonempty set V of p points (vertex) together with a prescribed set X of q unordered pairs of distinct points of V.
A hypergroup in the sense of Marty is a nonempty set H endowed by a hyperoperation * : H x H [right arrow] [P.sup.*](H) [1], the set of the entire nonempty set H, which satisfies the associative law and reproduction axiom.
(1) U = {[x.sub.1], [x.sub.2], ..., [x.sub.n]} is a nonempty set of n data objects, which is named as a universe;