The aim of this chapter is to introduce a new class of contra continuous functions, namely neutrosophic contra RW-continuous functions, in neutrosophic topological spaces. Further, the authors introduce neutrosophic almost RW-continuous function, neutrosophic almost contra RW-continuous function, and some of its properties have been discussed. Relationships with some other existing neutrosophic contra continuous functions have been analyzed. Furthermore, NRW-T0, NRW-T1, NRW-T2, and NRW-normal spaces have been introduced.
Top2. Terminologies
In this section some important basic preliminaries, and in particular, the work of Smarandache (Smarandache, 2002a) and Salama (Salama & Alblowi, 2012a) have been recalled.
Definition 2.1:(Smarandache, 2002a) Let X be a non-empty fixed set a Neutrosophic set (NS for short) A is an object having the form 
, x∈X where µA(x), σA(x), γA(x) which represents the degree of membership function, the degree of indeterminacy and the degree of non-membership function respectively of each element x∈X to the set A.
Remark 2.2: (Smarandache, 2002a) For the sake of simplicity A neutrosophic set A = {x, µA(x),σA(x),γA(x)>; x∈X} can be identified to be an ordered triple < µA,σA,γA>.
Definition 2.3:(Salama & Alblowi, 2012a) The neutrosophic subsets 0N and IN in X are defined as follows:
(1) 0
N = {<x, (0, 0, 1)>; x ∈X} (2) I
N = {<x, (1, 0, 0)>; x ∈X}
Definition 2.4: (Salama & Alblowi, 2012a) Let X be a nonempty set and neutrosophic sets A and B in the form A = {< x, (µA(x),σA(x),γA(x))>, x∈X} and B = {< x, (µB(x),σB(x),γB(x))>, x∈X}.
(1)
A ⊆ B ⇔ µ
A(x) ≤ µ
B(x), σ
A(x) ≤ σ
B(x), and γ
A(x) ≥ γ
B(x) ∀ x ∈ X
(2) 
= {<x, γ
A(x), σ
A(x), µ
A(x) >; x∈ X}
(3) A = B iff A ⊆ B and B ⊆ A.
(4) A ∩ B = < x, min(µ
A(x),µ
B(x)), min(σ
A(x),σ
B(x)), max(γ
A(x), γ
B(x)) >
(5) A ∪ B = < x, max(µ
A(x),µ
B(x)), max (σ
A(x),σ
B(x)), min (γ
A(x), γ
B(x)) >
Definition 2.5: (Salama & Alblowi, 2012a) Let {Aj: j∈J } be a arbitrary family of NS sets in X, then
(1)
∩ A
j = < x, ∧
j∈J
(x), ∧
j∈J
(x), ∨
j∈J
(x)