On Some Special Classes of Neutrosophic Crisp Topological Spaces

Abstract

Neutrosophic crisp sets have recently gained great importance in

mathematics and in all pure and exact mathematical subdisciplines due to their

significant role in solving real-life problems through the modeling of

mathematical systems, which has contributed to addressing many practical

problems across various fields. Based on neutrosophic crisp sets, the concept of

a neutrosophic crisp topological space has been introduced as a generalization of

classical topology.

In this academic and scientific research on neutrosophic crisp

topological spaces, five neutrosophic crisp topological spaces are

constructed, namely the , the Neutrosophic Crisp Topological Space

generated by a basis (ƝՄҪ ), the Neutrosophic Crisp semi-

Topological Space (ƝՄҪ

), the Neutrosophic Crisp

semi-

Topological Space (ƝՄҪ

), the Neutrosophic

Crisp pre-

Topological Space(ƝՄҪ

), and the

Neutrosophic Crisp pre-

Topological Space(ƝՄҪ

).

These four neutrosophic crisp topological spaces are constructed

through new definitions of the closure of a neutrosophic crisp set and

the interior of a neutrosophic crisp set. Furthermore, all classical

topological theorems, results, and relations that hold in these five

neutrosophic crisp topological spaces are proved, and illustrative

examples are provided for those that do not hold.