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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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