Neutrosophic Simply b-Open Set in Neutrosophic Topological Spaces

Abstract

In this paper, we procure the notions of neutrosophic simply b-open set, neutrosophic simply b-open cover, and neutrosophic simply b-compactness via neutrosophic topological spaces. Then, we establish some remarks, propositions, and theorems on neutrosophic simply
 b-compactness. Further, we furnish some counter examples where the result fails.

Topology on Rough Pentapartitioned Neutrosophic Set

“…A neutrosophic set V over a fixed set W is defined as follows: V = {(r, T V (r), I V (r), F V (r)): rW}, where T, I, F : W[0, 1] are the truth, indeterminacy and falsity membership functions respectively. Definition 2.2: [11]. Let W be a fixed set.…”

“…So, 0  T Z (r)+C Z (r)+G Z (r)+U Z (r)+F Z (r)  5, for all rW. Definition 2.3: [11]. Let W be a fixed set.…”

“…r,0,0,1,0,1): rW}; 0 PN = {(r,0,0,0,1,1): rW}; 0 PN = {(r,0,0,1,0,0): rW}; 0 PN = {(r,0,0,0,1,0): rW}; 0 PN = {(r,0,0,0,0,1): rW}; 0 PN = {(r,0,0,0,0,0): rW}. Remark 2.1: Clearly, 0 PN  X  1 PN , for every P-NS X over W. Definition 2.4: [11]. Let M={(r,T M (r),C M (r),G M (r),U M (r),F M (r)): rW} and N={(r,T N (r),C N (r), G N (r),U N (r),F N (r)): rW} be two P-NSs over W.…”

“…Das and Pramanik [10] also presented the neutrosophic -open set and neutrosophic -continuous functions. Recently, Das and Tripathy [15] introduced the notion of neutrosophic simply b-open set in neutrosophic topological space. Later on, Ozturk and Ozkan [23] grounded the concept of bi-topological space under the neutrosophic set environment.…”

“…Later on, Ozturk and Ozkan [23] grounded the concept of bi-topological space under the neutrosophic set environment. Thereafter, Das and Tripathy [14] presented the notion of pairwise neutrosophic b-open set via neutrosophic bi-topological space. Tripathy and Das [33] grounded the concept of pairwise neutrosophic b-continuous mappings via neutrosophic bi-topological space.…”