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... exists a preopen set ρ in X containing xε such that f (ρ) ≤ β. Therefore, we obtain yν ∈ µ and f (ρ) ∧ µ = ∅. This shows that G(f ) is fuzzy pre-co-closed. Theorem 28. If f : X → Y is fuzzy precontinuous and Y is fuzzy co-T1 , then G(f ) is fuzzy pre-co-closed in X × Y . Proof. Let (xε , yν ) ∈ (X × ...

... exists a preopen set ρ in X containing xε such that f (ρ) ≤ β. Therefore, we obtain yν ∈ µ and f (ρ) ∧ µ = ∅. This shows that G(f ) is fuzzy pre-co-closed. Theorem 28. If f : X → Y is fuzzy precontinuous and Y is fuzzy co-T1 , then G(f ) is fuzzy pre-co-closed in X × Y . Proof. Let (xε , yν ) ∈ (X × ...

Closed and closed set in supra Topological Spaces

... S-S continuous functions and S* - continuous functions. In 2010, O.R.Sayed and Takashi Noiri [10] introduced supra b - open sets and supra b continuity on topological spaces. In this paper, we use closed and closed set as a tool to introduce the concept of supra supra ...

... S-S continuous functions and S* - continuous functions. In 2010, O.R.Sayed and Takashi Noiri [10] introduced supra b - open sets and supra b continuity on topological spaces. In this paper, we use closed and closed set as a tool to introduce the concept of supra supra ...

Gδ–SEPARATION AXIOMS IN ORDERED FUZZY TOPOLOGICAL

... Definition 4. A family H of fuzzy Gδ -neighbourhoods of a point x is called a base for the system of all fuzzy Gδ -neighbourhood µ of x if the following condition is satisfied. For each fuzzy Gδ -neighbourhood µ of x and for each θ, with 0 < θ < µ(x) there exists µ1 ∈ H with µ1 ≤ µ and µ1 (x) > 0. D ...

... Definition 4. A family H of fuzzy Gδ -neighbourhoods of a point x is called a base for the system of all fuzzy Gδ -neighbourhood µ of x if the following condition is satisfied. For each fuzzy Gδ -neighbourhood µ of x and for each θ, with 0 < θ < µ(x) there exists µ1 ∈ H with µ1 ≤ µ and µ1 (x) > 0. D ...

Fuzzy Irg- Continuous Mappings

... Let X be a nonempty set. A family τ of fuzzy sets of X is called a fuzzy topology [2] on X if the null fuzzy set 0 and the whole fuzzy set 1 belongs to τ and τ is closed with respect to any union and finite intersection. If τ is a fuzzy topology on X, then the pair (X, τ) is called a fuzzy topologic ...

... Let X be a nonempty set. A family τ of fuzzy sets of X is called a fuzzy topology [2] on X if the null fuzzy set 0 and the whole fuzzy set 1 belongs to τ and τ is closed with respect to any union and finite intersection. If τ is a fuzzy topology on X, then the pair (X, τ) is called a fuzzy topologic ...

# Covering space

In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.