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عنوان البحث(Papers / Research Title)


Characterizations of Continuity and Compactness with Respect to Weak Forms of -Open Sets


الناشر \ المحرر \ الكاتب (Author / Editor / Publisher)

 
لؤي عبد الهاني جبار السويدي

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لؤي,عبد,الهاني,جبار,السويدي ,Characterizations of Continuity and Compactness with Respect to Weak Forms of -Open Sets , Time 07/02/2016 09:36:28 : كلية التربية للعلوم الصرفة

وصف الابستركت (Abstract)


We use the weak open sets defined by T. Noiri, A. Al-Omari, M. S. M. Noorani in [5], to define new weak types of continuity and compactness and prove some theorems about them

الوصف الكامل (Full Abstract)

Through out this paper , stands for topological space. Let be a topological space and a subset of . A point in is called condensation point of if for each in with in , the set U is un countable [3]. In 1982 the closed set was first introduced by H. Z. Hdeib in [3], and he defined it as: is closed if it contains all its condensation points and the open set is the complement of the closed set. Equivalently. A subset of a space , is open if and only if for each , there exists such that and is countable. The collection of all open sets of denoted form topology on and it is finer than . Several characterizations of closed sets were provided in [1, 3, 4, 6]. For a subset of , the closure of and the interior of will be denoted by and respectively. The interior of the set defined as the union of all open sets contained in .
In 2009 in [5] T. Noiri, A. Al-Omari, M. S. M. Noorani introduced and investigated new notions called open, open, open and open sets which are weaker than open set.

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