الفهرس 
Chapter1. IntroductionOnly 14 pages are availabe for public view
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Abstract
Several theories such as the theory of fuzzy sets [1], theory of intuitionists fuzzy sets [2], theory of interval mathematics [3, 4] and theory of rough sets [5] can be considered as mathematical tools for dealing with uncertainties.
In 1999, Molodtsov [6] initiated the theory of soft sets as a new mathematical tool for dealing with uncertainties. Maji et al. [7, 8] presented some new definitions on soft sets such as ”soft subset ”, ”the complement of a soft set” and discussed in detail the applications of soft set theory in the field of the decision making problems. Many researchers have contributed towards the basic notions of soft set theory [9- 20].
In 2011, Shabir and Naz [21] introduced the notion of soft topological spaces over an initial universe with a fixed set of parameters. They showed that a soft topological space gives a parameterized family of topological spaces. Also, they defined basic notions of soft open sets and soft closed sets, soft subspace, soft closure, soft neighborhood of a soft point and soft separation axioms and established their several properties. Later, many authors [22 - 47] continued to study the properties of soft topological spaces. They got many important results in soft topological spaces.
Ideals in topological spaces have been considered since 1933 [48]. This topic has won its importance by the paper of Vaidyanathasway [49] in1945.
The contributions of Dontchev, Hamlett and Jankovc ́ [50-53] in ideal topological spaces initiated the generalization of some important properties in general topology via topological ideals. The properties like decomposition of continuity, separation axioms, connectedness, compactness, and resolvability have been generalized using the concept of ideals in topological spaces [54-59].
In 2013, Şahin and Küçük [60] introduced the notion of soft ideal. This notion was studied by Kandil et al. [61] and some notions related to it were defined such as soft local functions, soft *-topology, soft semi-I-compact spaces and soft connected spaces. These concepts are studied to get new soft topologies from the original one, named soft topological spaces with soft ideal. Later many authors [62-70] have studied various concepts in soft ideal topological spaces. Şahin and Küçük
In this thesis some new topological concepts in soft ideal topological spaces were introduced and studied. This were done by generalizing the results obtained in [71-76] to the soft setting.
This thesis which consists of five chapters is organized as follows:
Chapter 1: This chapter is devoted to give an exposition of some needed definitions and theorems of soft sets, soft topological spaces and soft ideal topological space.
Chapter 2: In this chapter some results on soft pre ideal open sets were studied. Also, the concepts of a soft pre ideal neighborhood, a soft pre ideal limit point, a soft pre ideal frontier, a soft pre ideal exterior and a soft pre ideal border of a soft set are investigated. The results of this chapter are published in a research paper [77].
Chapter 3: A new class of soft sets called soft delta pre ideal open sets in soft ideal topological space related to the notion of soft pre ideal regular pre ideal open sets were introduced and studied. Soft separation axioms based on the soft delta pre ideal open sets were investigated. The results of this chapter was presented in the 32nd Conference on ’’ Topology and it’s Applications’’ July 24, 2019, Department of Mathematics, Faculty of Science, Helwan University, EGYPT [78].
Chapter 4: The properties of soft R-Ι ̃- closed sets, soft 〖 A〗_Ι ̃^*- sets were introduced and studied. Soft codense ideals also were characterized by these collections of sets. Furthermore, a decompositions of soft continuous mappings and soft 〖 A〗_Ι ̃^*- continuous mappings were given.
Chapter 5: In this chapter, more properties and characterizations of ψ-soft operator were given. Also, the concepts of ”equal [mod Ι ̃ ] ” and Bair soft sets were introduced. Also the relations between these concepts and ψ- soft operator were given. Furthermore, the concepts of ψ^*-soft operator and ψ^*-soft sets were introduced and studied. Furthermore, the concepts of *^ψ-soft operator and *^ψ-soft sets were introduced and some of their properties were studied [79].