Z-open sets in a Neutrosophic Topological Spaces

In this paper, introduce a neutrosophicopen sets in neutrosophic topological spaces. Also, discuss about near open sets, their properties and examplesZ-open set which is a union of neutrosophic P-open sets and neutrosophic δof a neutrosophicS Z-open set. Moreover, we investigate some of their basic properties and examples of neutrosophic Zinterior and Z-closure in a neutrosophic topological spaces.

Then (X,τN) is called a neutrosophic topological space (briefly, Nts) in X. The τN elements are called neutrosophic open sets (briefly, Nos) in X. A Ns C is called a neutrosophic closed sets (briefly, Ncs) iff its complement C c is Nos. Definition 2.4 [8] Let (X,τN) be Nts on X and L be an Ns on X, then the neutrosophic interior of L (briefly, Nint(L)) and the neutrosophic closure of L (briefly, Ncl(L)) are defined as Nint(L) = ∪{I : I ⊆ L & I is a Nos in X} Ncl(L) = ∩{I : L ⊆ I & I is a Ncs in X}. Definition 2. 5 [1] Let (X,τN) be Nts on X and L be an Ns on X. Then L is said to be a neutrosophic regular (resp. pre, semi, α & β) open set (briefly, Nros (resp. NPos, NSos, The complement of an NPos (resp. NSos, Nαos, Nros & Nβos) is called a neutrosophic pre (resp. semi, α, regular & β) closed set (briefly, NPcs (resp. NScs, Nαcs, Nrcs & Nβcs)) in X.
The family of all NδSos (resp. NδScs) of X is denoted by NδSOS(X) (resp. NδSCS(X)). Definition 2.8 [14] A set K is said to be a neutrosophic The family of all Neos (resp. Necs) of X is denoted by NeOS(X) (resp. NeCS(X)). 3 Neutrosophic Z-open sets in Nts Throughout the sections 3 & 4, let (X,τN) be any Nts. Let K and M be a Ns's in Nts.
It is also true for their respective closed sets.  (Ncl(H))). Therefore, Ncl(H) is NSo. Theorem 3.2 The statements are true.

Nos
Nδ S os N P os
Conversely, suppose K be a NZcs in X. Then, we have K ∈ ∩{A : K ⊆ A & A is a NZcs}. Hence, K ⊆ A implies K = ∩{A : K ⊆ A & A is a NZcs} = NZcl(K).
Similarly for K = NZint(K). Ξ Proposition 3. 4 Let K and L are in X, then (i) The proof is directly from definition.