A note on Spherical Continuity

In this paper, wedefine Spherical fuzzy continuity between Spherical fuzzy topological space and we characterize the concept.

As a generalization of a crisp set, the concept of fuzzy set was introduced by L.A. Zadeh [1]. The concept of fuzzy topological space was defined and few basic notions as open set, closed and continuity were generalized by Chang [8]. By changing a basic property of topology, another definition was given by Lowen [9].
A non-empty set X with τ , a collection of subsets of X satisfying conditions φ,X ∈ τ , arbitrary union of elements of τ is in τ and finite intersection of τ also belong to τ is said to be a Topological space. A non-empty fixed set X with τ , a collection of fuzzy subsets of X sustaining the criteria's 0, 1 ∈ τ , arbitrary union of elements of τ is in τ and finite intersection of τ also belong to τ is said to be a Fuzzy topological space [8].
The main crux of this paper is to define and characterize the concept of Spherical fuzzy continuity between Spherical fuzzy topological space.

2.Spherical Fuzzy Topological Space
In this section, we introduce the continuity of a function among Spherical fuzzy topological space.
Definition 2.1 Let X = φ be a set and let τ be a family of Spherical fuzzy subsets of X. If For any {A i } i∈tau , we have i∈τ A i ∈ τ where I is an arbitrary index set then τ is called a Spherical fuzzy topology on X.
The pair X ∈ τ is said to be Spherical Fuzzy Topological Space (SFTS) [10]. Each member of τ is called an open spherical fuzzy subset. The complement of an open spherical fuzzy subset is called a closed spherical fuzzy subset. As classical topologies or a fuzzy topological space, the family {1 s , 0 s } is called the indiscrete spherical fuzzy topological space and the topology that contains all spherical fuzzy subsets is called the discrete spherical fuzzy topological space. A Spherical fuzzy topology τ , is said to be coarser than a Spherical fuzzy topology τ 2 defined on same set if τ 1 ⊂ τ 2 .
Example 2.2 Let X=1,2. Consider the family of Spherical fuzzy subsets In this example (X, τ ) is a Spherical fuzzy topological space. Any fuzzy subset or picture fuzzy subset of a set can be considered as Spherical fuzzy subset, we observe that any fuzzy topological space or picture fuzzy topological space is a Spherical fuzzy topological space. But a spherical fuzzy topological space need not be a picture fuzzy topological space.
Instead of a neighbourhood of a fuzzy point, Chang [8]  and defined as Respectively, The truthiness, abstinence and falseness function of pre-image of B with respect to f is denoted by f −1 [B] are defined by The image and pre-image of A,B respectively are spherical fuzzy subset. Since mu A γ A and σ A are non-negative, is also a spherical fuzzy subset. Proposition 2.6 Let X and Y be 2 non-empty sets and let f : X → Y be a function. Then ) for any spherical fuzzy subset A of X.
(2) ⇒ (3) Let us assume (2) holds, A be a spherical fuzzy subset of X and let V be (

3) ⇒ (4) Assume (3) and let A be SFS of X and let V be a neighbourhood of f[A].
Problem (3), there exists a neighbourhood U of A such that U ⊂ f −1 (V ). Since U is a neighbourhood, by definition we have an open spherical fuzzy subset D of X, (4) ⇒ (1) By assuming (4), Let A be a spherical fuzzy subset of X and V, a neighbourhood of f(A). Terefore by (4) there exists an open spherical fuzzy subset D such that Following is a characterization of spherical fuzzy continuity, can also be used as the other definition of spherical fuzzy continuous function.