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Operations and its Applications On L-fuzzy Bi topological Spaces أحمد سعيد عبدالله العربي

:Abstract

In this and a subsequent paper, a new operation on the class of all L-fuzzy subsets of a universe endowed with a fuzzy topological space is introduced to generalize several characterization and properties of some fuzzy bitopological concepts such as a fuzzy interior operators and some new classes of fuzzy separation axioms. Also, the relation between these classes and the weaker and stronger forms in fuzzy bitopological spaces are investigated. Finally, we showed that these axioms are good extension in the sense of Lowen (1978) due to Lowen, in Part II this theory is applied on the mappings defined on L-fuzzy bitopological spaces

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On Extended Fuzzy Topologies أحمد سعيد عبدالله العربي

:Abstract

Basic results on extended fuzzy topologies are presented which are obtained in applying the theory of fuzzy stacks. In particular, the category EFTOP of extended-fuzzy topological spaces and several of its bireflective and bicoreflective subcategories are studied

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General Notions Related to Fuzzy Filters أحمد سعيد عبدالله العربي

:Abstract

  Basic results on L-fuzzy topology are presented which are obtained in applying the theory of fuzzy filters and the operations defined on the set of all L-fuzzy subsets endowed with an L-fuzzy topology. In particular , the category CSOF of all characterized spaces and several of its bireflective and bicoreflective subcategories are studied

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On Characterizing Notions of Characterized Spaces أحمد سعيد عبدالله العربي

:Abstract

Basic results on the characterized spaces are presented obtained in applying the theory of fuzzy filters devolped in [6] and using results given in [1]. There are mainly investigated notions defined for characterized spaces which can be used for their characteriztion. They are called characterizing notions. In some cases the notions we consider are characterizing under some assumptions on the characterized spaces. Examples of characterizing notions which do not need any assumption are those of φ1;2-fuzzy neighborhood of a fuzzy filter, of the φ1;2-interior of a fuzzy filter and of the set of φ1;2-inner points of a fuzzy filter. The notions of φ1;2-open fuzzy filter and of projectively φ1;2 open fuzzy fillter are characterizing for idempotent characterized spaces. Further characterizing notions are presented obtained by restricting to valued and superior principal fuzzy filters ...
Closdeness and Compacteness in Characterized Spaces أحمد سعيد عبدالله العربي

:Abstract

Contrary to the characterizing notions for characterized spaces develop in [2], we are investigated the notions which have the same invariance properaties and which, as is shown, only depend on φ1;2-converging fuzzy filter. Examples are the notions of φ1;2-adherence point, of projective φ1;2-closedness and of φ1;2-closedness of a fuzzy filter. By restricting to valued and superior principle fuzzy filters we get analogous notions for fuzzy sets. The φ1;2-closures of a fuzzy filter are defined in some sence complementarily to the notion of φ1;2-fuzzy neighborhood of a fuzzy filter. A further notion considered here which has the same invariance properaties and only depend on φ1;2-converging fuzzy filters is that of φ1;2-compactness. In general, φ1;2-compactness is defined for fuzzy filters. A fuzzy set is called φ1;2-compact if the related superior principle fuzzy filter is φ1;2-compact. The φ1;2-compactness of the whole space means the φ1;2-compactness of the constant fuzzy set with value 1. In the classical case of a topological space this is the usual compactness.There are generalizd some classical results on compactness. For instance, a generalized Tychonoff Theorem is presented ...
Mappings Between L-fuzzy Bitopological Spaces أحمد سعيد عبدالله العربي

:Abstract

In this paper, the operation on the class of all L-fuzzy subsets of a universe endowed with a fuzzy  topological space is applied to generalize several characterizations and properties of some fuzzy bitopological concepts such as fuzzy compactness, fuzzy continuity, fuzzy openness and fuzzy irreducible mappings.Also, the implications between each of these mappings and the weaker and stronger forms in fuzzy bitopological spaces are investigated. Finally, we showed that these concepts are good extension in the sense of [18] due to Lowen ...
Separation Axioms in Characterized Fuzzy Spaces أحمد سعيد عبدالله العربي

:Abstract

Basic results on fuzzy separation axioms in the characterized fuzzy spaces related to the fixed L-fuzzy topology are presented which are obtained in applying the general theory of fuzzy filters and the operations defined on the set of all L-fuzzy subsets endowed with an L-fuzzy topology. In particular, we using the notion of φ1,2-fuzzy neighborhood filter at a point x and the notion of φ1,2-fuzzy convergence to introduce and study the notions of characterized FTk-spaces and Fφ1,2-Tk spaces for k ∈ {0,1,2}. These axioms are related only the usual points and the ordinary subsets. In the classical case of L = {0,1}, φ1 = int and φ2 = 1 LX, these axioms are the usual ones. Many properties are fulfilled for these axioms analogous to the usual ones. Our axioms are generalized a lot of the weaker and stronger forms of the existing fuzzy separation axioms in fuzzy topological spaces. So many new special cases from these classes of fuzzy separation axioms are obtained by special choices for the operations φ1 and φ2 in Table (1). In [2], we introduced and study the notion of FRs axioms in characterized fuzzy spaces for s ∈ {2,3}  and we used it to study the notion of characterized FTk-spaces for k ∈ {3,4} ...
FUZZY REGULARITY AXIOMS AND FT2.5 AXIOMS IN CHARACTERIZED SPACES أحمد سعيد عبدالله العربي

:Abstract

In this paper, basic results on some type of luzzy regularity axioms in characterized spaces related to the fixed L-fuzzy topology are presented.These are obtained in applying the geaeral theory of fuzzy filters and the operations defined on the set of all L-fuzzy subsets endowed with an L-fuzzy topolos. The notion of φ1,2-fuzzy neighborhood filter at a point x is applied to introduced the notions of characterized FRk and Fφ1,2-Rk spaces for k ∈ {0, 1}. The axioms FT2.5 and Fφ1,2-T2.5 will be done by applying the notion of φ1,2-fuzzy convergence. Many new special cases from these classes of fuzzy regularity and FT2.5  axiorns are obtained by special choice for the operations φ1 and φ2 in Table (l ...
ON CHARACTERIZED FUZZY REGULAR AND FUZZY NORMAL SPACES أحمد سعيد عبدالله العربي

:Abstract

Basic resuirs on characterized fuzzy regulaxity and fuzzy normality axioms in characterized fuzzy spaces .related to the fixed L-fuzzy topology are presented. These are obteined in applying the general theory of fuzzy filters and the operations defined on the set of all L-fuzzy subsets endowed with an L-fuzzy topology. The notion of φ1,2-fuzzy neighborhood filter at a point o and at the ordinary subset are applied  to introduce the notions of characterized fuzzy regular and fuzzy normal spaces. Fuzzyφ1,2-regular and fuzzy φ1,2-normal spaces will be done by applied the notion of φ1,2-fuzzy convergence at the usual point and at the ordinary subset. By means of these notions the charcrterized FTs-spaces and Fφ1,2-Ts spaces for s € {3,4} are introduced and studied. Many new special cases from these classes are obtained by special choices for the operations φ1 and φ2 in Table (1 ...
Characterized Proximity L-spaces, Characterized Compact L-spaces and Characterized Uniform L-spaces أحمد سعيد عبدالله العربي

:Abstract

In this research work, three new spaces are proposed and investigated. The spaces are named   characterized proximity L-space, characterized compact L-space and characterized uniform L-space. The properties of such spaces are deeply studied. Some sort of relationship were introduced among such spaces and other published spaces resented by the author. The published spaces are named characterized FTs-spaces and characterized FRk-spaces ([2,3,4]), for s ∈ {0, 1,2,2.5,3 ,4} and k ∈{0,1,2,,3}. New properties were already added to the characterized FTs-spaces and to the characterized FRk-spaces. Moreover, the characterized proximity L-space, characterized compact L-space and characterized uniform L-space are classified according to the characterized FTs-spaces and the characterized FRk-spaces for s ∈ {0, 1,2,,4}  and k ∈{,2,,3}

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