الفهرس 
chapter 1Only 14 pages are availabe for public view
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Abstract
As a continuation to the study of neutrosophic initiated by Smarandach [55] in 1991. The aim of this thesis is twofold, in the first we develop the concepts of the neutrosophic crisp set introducing what we called the retract neutrosophic crisp set, the new proposed set is a retraction of any triple structured crisp set. Whereas we show the retraction of a neutrosophic crisp set coincides its corresponding star neutrosophic crisp set which defined by Salama et al [49]. The introduced set let to a construction of a retraction of the neutrosophic crisp topological spaces, called the retract neutrosophic topological spaces. As well as investigating some of its properties. The second aim of this thesis is introducing the concepts of neutrosophic smooth topological space, neutrosophic smooth cotopological space, neutrosophic smooth closure and neutrosophic smooth interior. Furthermore, we introduce the concepts of smooth neutrosophic pretopological space, smooth neutrosophic pretopological subspace, smooth neutrosophic interior mapping and smooth neutrosophic continuity. As well as investigating some properties.