Abstract

The notion of a subnexus based on NN-function (briefly, NN-subnexus) is introduced, and related properties are investigated. Also, the notions of NN-subnexus of type (α,β)(α,β), where (α,β)(α,β) is (∈,∈)(∈,∈), (∈,q)(∈,q), (∈,∈∨q)(∈,∈∨q), (q,∈)(q,∈), (q,q)(q,q), (q,∈∨q)(q,∈∨q), (¯¯¯¯∈,¯¯¯¯∈)(∈¯,∈¯) and (¯¯¯¯∈,¯¯¯¯∈∨¯¯¯q)(∈¯,∈¯∨q¯), are introduced, and their basic properties are investigated. Conditions for an NN-structure to be an NN-subnexus of type (q,∈∨q)(q,∈∨q) are given, and characterizations of NN-subnexus of type (∈,∈∨q)(∈,∈∨q) and (¯¯¯¯∈,¯¯¯¯∈∨¯¯¯q)(∈¯,∈¯∨q¯) are provided. Homomorphic image and preimage of NN-subnexus are discussed.

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