On prime spaces of neutrosophic extended triplet groups

Abstract This article aims to investigate the Zariski topology on the set of prime ideals of a weak commutative neutrosophic extended triplet group (NETG) N N , denoted by Prim ( N ) {\rm{Prim}}\left(N) . First, by giving an equivalent characterization of idempotent weak commutative NETGs, we show that a topological space X X is an S S SS -space if and only if X X is homeomorphic to the space Prim ( N ) {\rm{Prim}}\left(N) of some weak commutative NETG. In addition, we prove that there exists an adjunction between the dual category of weak commutative NETGs and the category of S S SS -spaces. Finally, we further study the categorical relation between idempotent weak commutative NETGs and that of S S SS -spaces, which leads to a conclusion that the category of idempotent weak commutative NETGs is equivalent to that of commutative idempotent semigroups.