The covering dimension of topological spaces is considered one of the most important dimensions functions in dimension theory, and the locally covering dimension is no less important than it.  Also, it closely related to covering dimension and other topological dimensions, so, in this paper, we study some interesting properties of zero and local covering dimension of fuzzy neutrosophic topological spaces, first, we establish a zero dimensionality and covering dimension of fuzzy neutrosophic spaces then we find the locally covering dimension of fuzzy neutrosophic regular spaces. Furthermore, a quantity of appealing properties and characterizations of subset theorem, fuzzy neutrosophic local homeomorphism and other related properties are studied.

Keywords:. Fuzzy neutrosophic topology, fuzzy neutrosophic covering dimension, fuzzy neutro- sophic locally covering dimension, zero-dimensionality