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عنوان البحث(Papers / Research Title)


Turing Point of proper Ideal


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

 
لؤي عبد الهاني جبار السويدي

Citation Information


لؤي,عبد,الهاني,جبار,السويدي ,Turing Point of proper Ideal , Time 14/12/2016 10:09:13 : كلية التربية للعلوم الصرفة

وصف الابستركت (Abstract)


In this paper we introduce and study the concepts of a new class of points, namely turing points of proper ideal and some of their properties are analyzed

الوصف الكامل (Full Abstract)

Ideal in topological spaces have been considered since 1930. This topic won its importance by
the paper of Vaidyanathaswamy [7] and Kuratwoski [6]. Applications to various fields were further
investigated by Jankovi? and Hamlett [3]; Dontchev et al. [2]; Mukherjee et al. [4]; Arenas et al. [5];
Navaneethakrishnan et al. [1]; Nasef and Mahmoud [8], etc. In this paper We used only the proper ideal
to work , ideal bace, turing point, finer than, and maximal ideal to prove continuous, compactness, ????
space and ideal net. Let ???? , ???? be a topological space, by ???? we will denote the open neighborhood
system at a point ?? ?? ??.
A set ? is said to be directed if and only if there is a relation ?? on ? satisfying, (i) ?? ?? ?? for each
?? ?? ?, (ii) if ???? ?? ???? and ???? ?? ???? then ???? ?? ????, (iii) if ????, ???? ?? ?, then there is ???? ?? ? such that
???? ?? ???? and ???? ?? ???? [9]. A net in a set ?? is a function ?? on a directed set into ?? [9]. By ????????????? we
will denote the net ??. Let ?? ?? ??, a net ?? on ?? is said to be eventually in ?? iff there exists ???? ?? ? such
that ?? ?? ???? implies that ???? ?? ??. A net ????????????? convergent to ???? ?? ?? iff its eventually for each
?? ?? ?????? and denoted by ????????????? ?? ????. A topological space ?? is compact if and only if every class ????????
of closed subsets of ?? which satisfies the finite intersection has, itself, a non-empty intersection [9]

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