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Register a new userNα-Open Sets and Sα-Open Sets in Tri-topological Spaces
المجموعات المفتوحة من النمط Nα و المجموعات المفتوحة من النمط Sα في الفضاءات التبولوجية الثلاثية
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Aِl-Baath University ورقة بحثية
Publication date
2017
fields
Mathematics
and research's language is
العربية
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قدمنا في هذا البحث، أربعة أنواع جديدة من المجموعات المفتوحة و المغلقة في الفضاءات التبولوجية الثلاثية، حيث أدخلنا تعريف المجموعات المفتوحة من النمط Nα و المجموعات المغلقة من النمط Nα في الفضاءات التبولوجية الثلاثية، و عرفنا المجموعات المفتوحة من النمط Sα, و المجموعات المغلقة من النمط Sα في هذه الفضاءات، و درسنا الخصائص الأساسية لهذه الأنواع الجديدة من المجموعات، و أوجدنا العلاقة بينها و بين المجموعات المفتوحة، المغلقة في هذه الفضاءات التبولوجية الثلاثية. ثم استخدمنا هذا المفهوم الجديد للمجموعات المفتوحة و المغلقة في تعريف لصاقة و داخلية مجموعة، حيث عرفنا لصاقة و داخلية مجموعة من النمط Nα و ذلك بالاعتماد على هذه الأصناف الجديدة من المجموعات المفتوحة و المغلقة، و أوجدنا الخصائص الأساسية للصاقة و الداخلية من النمط Nα.
In this paper we introduced four new types of open and closed sets in tri-topological spaces, where we have introduced the definition of open sets of the pattern Nα and closed sets of the pattern Nα in tritopological spaces, as the we know from the open sets of the pattern Sα and closed sets of the pattern Sα in these spaces, and we studied the basic properties of these new types of sets, as the we have created the relationship between them and open and closed sets in these tri-topological spaces. Then use this new concept of open and closed sets in the definition of closure and interior set, where we know the closure and interior set of the pattern Nα by relying on these new varieties of open and closed sets, we also found the basic properties of closure and the interior of the pattern Nα.
References used
Kelly, J. C. (1963), Bitopological spaces, Proc. London Math. Soc.,No.13, 71-89
Kovar,M. M. (2000), On 3-Topological Version Of q- Regularity, Internat. J. Math. & Math. Sci, Vol.23, No.6, 393- 398
Mrsevic and Reilly,I. L. (1996), Covering and Connectedness Properties of a Topological Space and it is Associated Topology of α-subsets, Indian J. Pure Appl. Math, Vol.27, No.10, 995- 1004
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In this paper we introduced four new types of open and closed sets in tri-topological spaces, where we have introduced the definition of open sets of the pattern N and closed sets of the pattern N in tri-topological spaces, as the we know from the op
en sets of the pattern S and closed sets of the pattern S in these spaces, and we studied the basic properties of these new types of sets, as the we have created the relationship between them and open sets and closed in these tri-topological spaces. Then use this new concept of open and closed sets in the definition of closure and interior set, where we know the closure and interior set of the pattern N by relying on these new varieties of open and closed sets, we also found the basic properties of closure and the interior of the pattern N.
In this paper we introduced new types of open and closed sets in bitopological
spaces, where we have introduced the definition of open
sets.
In this paper we introduced new types of open and closed sets in Quad-topological spaces, where we have introduced the definition of open sets of the pattern N and closed sets of the pattern N in Quad-topological spaces, as the we know from the open
sets of the pattern S and closed sets of the pattern S in these spaces, and we studied the basic properties of these new types of sets, as the we have created the relationship between them and open sets and closed in these Quad-topological spaces. Then use this new concept of open and closed sets in the definition of closure and interior set, where we know the closure and interior set of the pattern N by relying on these new varieties of open and closed sets, we also found the basic properties of closure and the interior of the pattern N.
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