عنوان البحث(Papers / Research Title)
Using ?-Operator to Formulate a New Definition of Local Function
الناشر \ المحرر \ الكاتب (Author / Editor / Publisher)
لؤي عبد الهاني جبار السويدي
Citation Information
لؤي,عبد,الهاني,جبار,السويدي ,Using ?-Operator to Formulate a New Definition of Local Function , Time 07/02/2016 08:55:44 : كلية التربية للعلوم الصرفة
وصف الابستركت (Abstract)
In this paper, we use ?-operator in order to get a new version of local function. The concepts of maps, dense, resolvable and Housdorff have been investigated in this paper, as well as modified to be useful in general.
الوصف الكامل (Full Abstract)
As requirements for our work, we define here the following concepts sequentially: Ideal space, local function, Kuratowski closure, dense, T*-dense, I-dense, codense, ?-operator, resolvable, I-open, pre-I-open, scattered set and Housdorff space. We start define the ideal space. Let (X, T) be a topological space with no separation properties assumed. The subject of ideal topological space has been studied by (Kuratowski, 1966) and (Vaidyanathaswamy, 1960). An ideal I on a topological space (X, T) is a nonempty collection of subsets of X which satisfies the following two conditions: )1) If A ? I and B ? A, then B? I (heredity). (2) If A? I and B? I, then A? B? I (finite additivity). Moreover a ?-ideal on a topological space (X, T) is an ideal which satisfies (1), (2) and the following condition: 3.If {Ai : i = 1,2,3,….} ? I, then ? {Ai : i =1,2,3,….} ? I (countable additivity
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