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Register a new userNew types of Open Sets and Closed Sets in bi-topological Spaces
انماط جديدة من المجموعات المفتوحة و المغلقة في الفضاءات التبولوجية الثنائية
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Aِl-Baath University ورقة بحثية
Publication date
2017
fields
Mathematics
and research's language is
العربية
Created by
Shamra Editor
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أوجدنا في هذا البحث، نوعاً جديداً من المجموعات المفتوحة و المجموعات المغلقة في الفضاءات التبولوجية الثنائية.
In this paper we introduced new types of open and closed sets in bitopological spaces, where we have introduced the definition of open sets.
References used
Kelly, J. C. (1963), Bitopological spaces, Proc. London Math. Soc.,No.13, 71-89
Jabbar ,N. A. and Nasir, A. I. (2010), Some Types of Compactness in Bitopological Spaces, Ibn AL-Haitham J. For Pure & Appl. Sci., Vol.23, No.1, 321-327
Gharibah ,T. and Alhamido ,R. Kh. (2017), Nα-Open Sets and Sα-Open Sets in Tri-topological Spaces, Journal of Albaath University., Vol. 39
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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.
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.
We prove that the sum A + B of closed subspaces A and B of the inverse
limit of finite dimensional vector spaces, V = limVn (n ∈ N) over an
algebraically closed field of characteristic 0 is closed.
We extend also the basic fact that every ideal of a finite dimensional
semisimple Lie algebra has a unique complement to the case of closed ideals of
prosemisimple Lie algebras.
This paper introduces a generalization of the concept of Set category
introduced in [10] by constructing the category - whose objects are
small ℒ - fuzzy sets in which the characteristic functions takes its values from
a complete distributive latt
ice, and its arrows are ℒ - fuzzy maps. After that
we construct a functor - between these two categories, in a
way that forgets the fuzziness of sets and maps, and formalizing the inclusion
functor - .
In addition, we study of the applications of universal arrows in category
- , and getting back to the classical state and comparing it with that
introduced in [10].
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