# empty set

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Related to Non-empty set: Proper subset

## empty set

Mathematics
The set that has no members or elements.
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Let X be a non-empty set and the NCSs C & D in the form C = <[C.sub.1], [C.sub.2], [C.sub.3]>, D = <[D.sub.1], [D.sub.2], [D.sub.3]> then we may consider two possible definitions for subsets C [subset not equal to] D, may be defined in two ways :
If [P.sub.C](x) is a non-empty set for each x in X, we say the subset C is proximinal in X.
Let X be a non-empty set. A fuzzy subset [mu] of X is a function from X into the closed unit interval [0, 1].
Let x be a non-empty set, and NCSS a and b in the form A = <[A.sub.1], [A.sub.2], [A.sub.3])>, B = <[B.sub.1], [B.sub.2], [B.sub.3])> with
Let be a non-empty set. A fuzzy set in X is a function with domain and values in .
A 4-tuple (B, A, L, R) is said to be a generalized onesided formal context if B is a non-empty set of objects, A is a non-empty set of attributes, L: A [right arrow] CL is a mapping from the set of attributes to the class of all complete lattices.
Let X be a non-empty set and [mu] be a collection of subsets of X.
A non-empty set A [subset] E is said to be totally antiproximinal if, for every norm [parallel] * [parallel] on E, every x [member of] E \ A and every y [member of] A, one has
The previous species are related by the following proposition, where X is the species of singleton, which associates to every singleton s itself and the empty set otherwise, and Comm is the species of non-empty sets, which associates to every non-empty set S the set {S} and the empty set otherwise:
A non-empty set M is said to be a l-module over a ring R, if it is equipped with the binary operation +, s.m and binary relation [less than or equal to] defined on it and satisfy the following condition
A BF-algebra is a non-empty set X with a consonant 0 and a binary operation * satisfying the following axioms:

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