The conception belonging to fuzzy sets was proposed by Zadeh [25]. Subsequently, the fuzzy sets along with the concept of fuzzy logic are used extensively in various applications implicating uncertainty. Although, it is examined that there still endure few situations which are not enclosed by fuzzy sets. Later, the fuzzy set exhibits as the conception based on the intuitionistic fuzzy set by Atannassov [5]. The fuzzy set is characterized by the membership function. Still, it is not possible to construct a membership function for each state. To meet this need, Al-Nafee, Al-Hamido, and Smarandache  [3] characterized the neutrosophic set approach for solving problems connecting imprecise, ambiguous together with inconsistent data. Neutrosophic topological space exhibits an expansion based on intuitionistic topological space along with each triplet set in the neutrosophic topological space consists of membership, indeterminacy along with non- membership values. In this article, a unique conception based on the neutrosophic SβF -Ti (i = 0, 1, 2, 3, 4) spaces in neutrosophic topological spaces are proposed. Further, many characterizations of neutrosophic SβF -Ti (i = 0, 1, 2, 3, 4) spaces are studied and discussed. In addition, many theorems are proved with the counter examples. In Figure 1, the interrelationship between neutrosophic SβF -Ti (i = 0, 1, 2, 3, 4) spaces are studied and discussed with suitable illustration.