Neutrosophic µ-Topological spaces

Abstract

In this paper, the concept of neutrosophic µ−topological spaces is introduced. We define and study
the properties of neutrosophic µ−open sets, µ−closed sets, µ−interior and µ−closure. The set of all generalize
neutrosophic pre-closed sets GNP C(τ ) and the set of all neutrosophic α-open sets in a neutrosophic topological
space (X, τ ) can be considered as examples of generalized neutrosophic µ−topological spaces. The concept
of neutrosophic µ − continuity is defined and we studied their properties. We define and study the properties of neutrosophic µ − compact, µ-Lindel¨of and µ-countably compact spaces. We prove that for a countable
neutrosophic µ-space X: µ-countably compactness and µ-compactness are equivalent. We give an example of
a neutrosophic µ-space X which has a neutrosophic countable µ-base but it is not neutrosophic µ-countably
compact .