A neutrosophic crisp topology (NCT) on a non-empty set
X is a family T of neutrosophic crisp subsets in X satisfying the following axioms :
An intuitionistic fuzzy set (briefly IFS) A is a non-empty set
X is an object having the form
Let B be a non-empty set
and L(a) be a system of complete lattices.
Let X ba a non-empty set
and [lambda] be the generalized topology on X and A [subset or equal to] X.
Separating these edges, we obtain a non-empty set
of hollow hypertrees with edges decorated by [??].
A non-empty set
M is said to be a l-module over a ring R, if it is equipped with binary operation +, s.m, [disjunction] and [conjunction] defined on it and satisfy the following conditions
A fuzzy subset [mu] in a non-empty set
X is a function [mu]: X [right arrow] [0,1].
Definition 2.1 : Let V be a finite non-empty set
. Then a fuzzy subset of V is a mapping [mu]:V [right arrow] [0,1] which assigns to each element [member of] V, a degree of membership, 0 [less than or equal to] [mu](v) [less than or equal to] 1.
Definition 1: An ordered pair (S, -), with S a non-empty set
and - being a binary operation on S, is called a subtractive groupoid if (1.) (a - b) - (c - d) = (d - b) - (c - a) for all a, b, c, d in S and (2.) there exists an element 0 in S such that a - 0 = a for all a in S and a - b = 0 if and only if a = b.
An assignment is said to satisfy a diagram D if and only if it satisfies all the representing facts of D, where an assignment satisfies the representing facts if, basically, any shaded region is assigned the empty set and any region with an x-sequence in it is assigned a non-empty set
4.1 Definition : A bipolar single-valued neutrosophic topology on a non-empty set
X is a [tau] of BSVN sets satisfying the axioms
Hence using the injectivity of j, the non-empty set
F(S) is contained in the fixed point set of S; which proves the existence of a common fixed point.