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Quad-topological Space And New Types Of Open and closed sets

الفضاءات التبولوجية الرباعية وأنماط جديدة من المجموعات المفتوحة والمغلقة

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 Publication date 2018
  fields Mathematics
and research's language is العربية
 Created by Al-Hamido Riad




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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.

References used
Alhamido ,R. Kh. and Imran, Q. H. (2017), "N-Open Sets and S-Open Sets in Tri-topological Spaces", University of Babyion J. For Pure & Appl. Sci., Vol.25, No.5.
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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 Nα and closed sets of the pattern Nα in tritopological spaces, as the we know from th e 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.
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.
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