Topology on Quadripartitioned Neutrosophic Sets

The focus of this paper is to introduce the notion of quadripartitioned neutrosophic topology (Q-NT) on quadripartitioned neutrosophic sets (Q-NS). In this paper, we define quadripartitioned neutrosophic closure, quadripartitioned neutrosophic interior operator of Q-NSs in quadripartitioned neutrosophic topological space (Q-NTS) and investigate several properties of them. Again, we introduce quadripartitioned neutrosophic semi-open (Q-NSO) set, quadripartitioned neutrosophic pre-open (Q-NPO) set, quadripartitioned neutrosophic b-open (Q-N-b-O) set, and quadripartitioned neutrosophic [alpha]-open (Q-N[alpha]-O) set in Q-NTSs. Further, we furnish some suitable examples and prove some basic results on Q-NTS. Keywords: Quadripartitioned Neutrosophic Set; Q-NT; Q-NTS; Quadripartitioned-Neutrosophic Closure; Quadripartitioned-Neutrosophic Closure; Q-NPO; Q-N[alpha]-O.