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Properties of Pre- -Open Sets and Mappings
Properties of Pre- -Open Sets and Mappings

ON FUZZY ALMOST CONTRA γ-CONTINUOUS FUNCTIONS K
ON FUZZY ALMOST CONTRA γ-CONTINUOUS FUNCTIONS K

FUZZY SEMI α-IRRESOLUTE FUNCTIONS 1. Introduction The fuzzy
FUZZY SEMI α-IRRESOLUTE FUNCTIONS 1. Introduction The fuzzy

view full paper - International Journal of Scientific and Research
view full paper - International Journal of Scientific and Research

PDF
PDF

... 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 × ...
Fuzzy Proper Mapping
Fuzzy Proper Mapping

ON Compactly fuzzy
ON Compactly fuzzy

On the forms of continuity for fuzzy functions
On the forms of continuity for fuzzy functions

The sums of the reciprocals of Fibonacci polynomials and Lucas
The sums of the reciprocals of Fibonacci polynomials and Lucas

... (x) are defined by Fn+2(x) = xFn+1(x) + Fn(x), n ≥ 0 with the initial values F0(x) = 0 and F1(x) = 1; Ln+2(x) = xLn+1(x) + Ln(x), n ≥ 0 with the initial values L0(x) = 2 and L1(x) = x. For x = 1 we obtain the usual Fibonacci numbers and Lucas numbers. Let ...
on fuzzy weakly semiopen functions
on fuzzy weakly semiopen functions

Fuzzy Regular Compact Space
Fuzzy Regular Compact Space

Totally Somewhat Fuzzy Continuous and Totally Somewhat Fuzzy
Totally Somewhat Fuzzy Continuous and Totally Somewhat Fuzzy

UTILIZING SUPRA α-OPEN SETS TO
UTILIZING SUPRA α-OPEN SETS TO

Fuzzy Irg- Continuous Mappings
Fuzzy Irg- Continuous Mappings



FUZZY r-REGULAR OPEN SETS AND FUZZY ALMOST r
FUZZY r-REGULAR OPEN SETS AND FUZZY ALMOST r

on fuzzy ˛-continuous multifunctions
on fuzzy ˛-continuous multifunctions

CHARACTERIZATIONS OF FUZZY α
CHARACTERIZATIONS OF FUZZY α

On Soft πgb-Continuous Functions in Soft Topological Spaces
On Soft πgb-Continuous Functions in Soft Topological Spaces

The Natural Criteria in Set-Valued
The Natural Criteria in Set-Valued

On Fuzzy γ - Semi Open Sets and Fuzzy γ - Semi
On Fuzzy γ - Semi Open Sets and Fuzzy γ - Semi

ON FUZZY NEARLY C-COMPACTNESS IN FUZZY TOPOLOGICAL
ON FUZZY NEARLY C-COMPACTNESS IN FUZZY TOPOLOGICAL

Topological dualities and completions for (distributive) partially ordered sets Luciano J. González
Topological dualities and completions for (distributive) partially ordered sets Luciano J. González

Soft ̃ Semi Open Sets in Soft Topological Spaces
Soft ̃ Semi Open Sets in Soft Topological Spaces

Closed and closed set in supra Topological Spaces
Closed and closed set in supra Topological Spaces

1 2 3 4 5 ... 211 >

Brouwer fixed-point theorem



Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f mapping a compact convex set into itself there is a point x0 such that f(x0) = x0. The simplest forms of Brouwer's theorem are for continuous functions f from a closed interval I in the real numbers to itself or from a closed disk D to itself. A more general form than the latter is for continuous functions from a convex compact subset K of Euclidean space to itself.Among hundreds of fixed-point theorems, Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics.In its original field, this result is one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem and the Borsuk–Ulam theorem.This gives it a place among the fundamental theorems of topology. The theorem is also used for proving deep results about differential equations and is covered in most introductory courses on differential geometry.It appears in unlikely fields such as game theory. In economics, Brouwer's fixed-point theorem and its extension, the Kakutani fixed-point theorem, play a central role in the proof of existence of general equilibrium in market economies as developed in the 1950s by economics Nobel prize winners Kenneth Arrow and Gérard Debreu.The theorem was first studied in view of work on differential equations by the French mathematicians around Poincaré and Picard.Proving results such as the Poincaré–Bendixson theorem requires the use of topological methods.This work at the end of the 19th century opened into several successive versions of the theorem. The general case was first proved in 1910 by Jacques Hadamard and by Luitzen Egbertus Jan Brouwer.
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