A Generalization of Subnexuses Based on <i>N</i>-Structures

Abstract

In this paper, we generalize the concepts of N-subnexuses of types (is an element of, q), (is an element of, is an element of boolean OR q) and (q, is an element of boolean OR q), and introduce the notions of N-subnexuses of types (is an element of, q(k)), (is an element of, is an element of boolean OR q(k)) and (q, is an element of boolean OR q(k)). We investigate their basic properties, characterize subnexuses by N-subnexuses of type (is an element of, is an element of boolean OR qk()), and give some characterizations for N-subnexuses of types (is an element of, q(k)) and (q, is an element of boolean OR q(k)). Moreover, we define N-subnexuses of type ((is an element of) over bar, (is an element of) over bar boolean OR(q(k)) over bar) and discuss on their different properties.