On the forms of continuity for fuzzy functions
... Proof. Let µ be any fuzzy open set in Y . Since Y is fuzzy PΣ , there exists a family Ψ whose members are fuzzy regular closed set of Y such that µ = ∨{ρ : ρ ∈ Ψ}. Since f is fuzzy almost contra-β-continuous, f −1 (ρ) is fuzzy β-open in X for each ρ ∈ Ψ and f −1 (µ) is fuzzy β-open in X. Therefore, ...
... Proof. Let µ be any fuzzy open set in Y . Since Y is fuzzy PΣ , there exists a family Ψ whose members are fuzzy regular closed set of Y such that µ = ∨{ρ : ρ ∈ Ψ}. Since f is fuzzy almost contra-β-continuous, f −1 (ρ) is fuzzy β-open in X for each ρ ∈ Ψ and f −1 (µ) is fuzzy β-open in X. Therefore, ...
SOME STRONGER FORMS OF FUZZY CONTINOUS MAPPINGS 1
... there exists a fuzzy open set V such that V U cl V . Complement of a fuzzy semi open set is called fuzzy semi cloed. FSO(X ) denotes the family of all fuzzy semi open sets of X . S -int U (semi interior of U ) is dened as the suprimum of all fuzzy semi open sets contained in U and S -cl U (semi ...
... there exists a fuzzy open set V such that V U cl V . Complement of a fuzzy semi open set is called fuzzy semi cloed. FSO(X ) denotes the family of all fuzzy semi open sets of X . S -int U (semi interior of U ) is dened as the suprimum of all fuzzy semi open sets contained in U and S -cl U (semi ...
Fuzzy Proper Mapping
... The concept of fuzzy sets and fuzzy set operation were first introduced by ( L. A. Zadeh ). Several other authors applied fuzzy sets to various branches of mathematics . One of these objects is a topological space .At the first time in 1968 , (C .L. Chang) introduced and developed the concept of fuz ...
... The concept of fuzzy sets and fuzzy set operation were first introduced by ( L. A. Zadeh ). Several other authors applied fuzzy sets to various branches of mathematics . One of these objects is a topological space .At the first time in 1968 , (C .L. Chang) introduced and developed the concept of fuz ...
view full paper - International Journal of Scientific and Research
... Let X be a non empty set and I= [0,1]. A fuzzy set on X is a mapping from X in to I. The null fuzzy set 0 is the mapping from X in to I which assumes only the value is 0 and whole fuzzy sets 1 is a mapping from X on to I which takes the values 1 only. The union (resp. intersection) of a family {Aα: ...
... Let X be a non empty set and I= [0,1]. A fuzzy set on X is a mapping from X in to I. The null fuzzy set 0 is the mapping from X in to I which assumes only the value is 0 and whole fuzzy sets 1 is a mapping from X on to I which takes the values 1 only. The union (resp. intersection) of a family {Aα: ...
... present paper, we introduce and characterize the notion of fuzzy L-Hausdorff spaces which is a generlization of some fuzzy concepts by using a fuzzy L-open sets , we also define the class of fuzzy irresolute functions via fuzzy topological ideals and investigate its relation to fuzzy L-Hausdorff spa ...
Topolog´ıa Algebraica de Espacios Topológicos Finitos y Aplicaciones
... The main goal of this Thesis is to study and to delve deeper into the development of the theory of finite spaces and to investigate their applications to the homotopy theory and simple homotopy theory of polyhedra and general topological spaces. We use, in particular, some of the results that we obt ...
... The main goal of this Thesis is to study and to delve deeper into the development of the theory of finite spaces and to investigate their applications to the homotopy theory and simple homotopy theory of polyhedra and general topological spaces. We use, in particular, some of the results that we obt ...
General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.The fundamental concepts in point-set topology are continuity, compactness, and connectedness: Continuous functions, intuitively, take nearby points to nearby points. Compact sets are those that can be covered by finitely many sets of arbitrarily small size. Connected sets are sets that cannot be divided into two pieces that are far apart. The words 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using open sets, as described below. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space.Metric spaces are an important class of topological spaces where distances can be assigned a number called a metric. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces.