Abstract
In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets. In addition, we discuss some applications of generalized neutrosophic pre-closed sets, namely neutrosophic p T 1 2 space and neutrosophic g p T 1 2 space. The concepts of generalized neutrosophic connected spaces, generalized neutrosophic compact spaces and generalized neutrosophic extremally disconnected spaces are established. Some interesting properties are investigated in addition to giving some examples.
Highlights
Zadeh [1] introduced the notion of fuzzy sets
Atanassov [4] introduced the notion of intuitionistic fuzzy sets (IFs)
Coker [6] introduced the notion of intuitionistic fuzzy topological space by using the notion of (IFs)
Summary
Zadeh [1] introduced the notion of fuzzy sets. After that, there have been a number of generalizations of this fundamental concept. Mathematics 2018, 7, 1 connected space, generalized neutrosophic compact space and generalized neutrosophic extremally disconnected spaces are introduced and established in Section 6 and some of their properties in neutrosophic topological spaces are studied This class of sets belongs to the important class of neutrosophic generalized open sets which is very useful in the deepening of our understanding of some special features of the already well-known notions of neutrosophic topology and proves useful in neutrosophic multifunction theory in neutrosophic economy and in neutrosophic control theory. The applications are vast and the researchers in the field are exploring these realms of research
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