• COMPACTNESS IN FUZZY NEAR-FIELD SPACES (CF-NF-S)

Abstract

Since earlier approaches to compactness in fuzzy spaces have serious limitations, we propose a new definition of fuzzy near-field spaces compactness. In doing so, after in depth study about near-rings, near-fields and generating near-fields, various near-fields over K-algebraic theory we observe that it is possible to have degrees of compactness, which we call b-compactness (b is a member of a designated lattice). We obtain a Tychnoff Theorem for an arbitrary product of b-compact fuzzy near-field spaces and a 1-point compactification. We prove that the fuzzy unit interval is b-compact.

Further we can extend the same to completeness in Fuzzy near-field spaces which is an ultimate to every near-field space in general so that we can generalize the feature of compactness leads to completeness of a Fuzzy near-field space.