[1] **viXra:1410.0132 [pdf]**
*submitted on 2014-10-22 17:33:09*

**Authors:** A. A. Salama, Said Broumi, Florentin Smarandache

**Comments:** 8 Pages.

The focus of this paper is to propose a new
notion of neutrosophic crisp sets via neutrosophic crisp
ideals and to study some basic operations and results in
neutrosophic crisp topological spaces. Also,
neutrosophic crisp L-openness and neutrosophic crisp Lcontinuity
are considered as a generalizations for a crisp
and fuzzy concepts. Relationships between the above
new neutrosophic crisp notions and the other relevant
classes are investigated. Finally, we define and study
two different types of neutrosophic crisp functions.
Index Terms—Neutrosophic Crisp Set; Neutrosophic
Crisp Ideals; Neutrosophic Crisp L-open Sets;
Neutrosophic Crisp L- Continuity; Neutrosophic Sets.
I. INTRODUCTION
The fuzzy set was introduced by Zadeh [20] in 1965,
where each element had a degree of membership. In
1983 the intuitionstic fuzzy set was introduced by K.
Atanassov [1, 2, 3] as a generalization of fuzzy set,
where besides the degree of membership and the degree
of non- membership of each element. Salama et al [11]
defined intuitionistic fuzzy ideal and neutrosophic ideal
for a set and generalized the concept of fuzzy ideal
concepts, first initiated by Sarker [19]. Smarandache [16,
17, 18] defined the notion of neutrosophic sets, which is
a generalization of Zadeh's fuzzy set and Atanassov's
intuitionistic fuzzy set. Neutrosophic sets have been
investigated by Salama et al. [4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15]. In this paper is to introduce and study some
new neutrosophic crisp notions via neutrosophic crisp
ideals. Also, neutrosophic crisp L-openness and
neutrosophic crisp L- continuity are considered.
Relationships between the above new neutrosophic crisp
notions and the other relevant classes are investigated.
Recently, we define and study two different types of
neutrosophic crisp functions.
The paper unfolds as follows. The next section briefly
introduces some definitions related to neutrosophic set
theory and some terminologies of neutrosophic crisp set
and neutrosophic crisp ideal. Section 3 presents
neutrosophic crisp L- open and neutrosophic crisp Lclosed
sets. Section 4 presents neutrosophic crisp L–
continuous functions. Conclusions appear in the last section.

**Category:** Topology