La continuidad entre espacios topológicos difusos
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Date
2013
Authors
Journal Title
Journal ISSN
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Publisher
Universidad Nacional de Trujillo
Abstract
La continuidad de una funci on de nida entre espacios topol ogicos cl asicos es un_x000D_
concepto topol ogico fundamental y de gran importancia para el desarrollo de las_x000D_
matem aticas y de sus aplicaciones. Sin embargo, debido a la complejidad del mundo_x000D_
real y de la imprecisi on contenida en muchos fen omenos de la naturaleza estos se describen_x000D_
o explican mejor mediante los conjuntos difusos, los que fueron introducidos_x000D_
por el ingeniero L. Zadeh (1965) [7]._x000D_
El concepto de conjunto difuso generaliza el concepto de conjunto cl asico. Un conjunto_x000D_
difuso A en un universo X est a asociado a una funci on A : X ! [0; 1] que_x000D_
asigna a cada elemento x de X un n umero real A(x) en [0; 1] llamado \grado de_x000D_
pertenencia" del elemento x al conjunto A. Un mayor grado de pertenencia re_x000D_
eja_x000D_
un sentido de pertenencia \m as" fuerte al conjunto A._x000D_
Este trabajo se basa en la teor a de los espacios topol ogicos difusos introducidos en_x000D_
1968 por Chang [1] y est a orientado a extender al contexto difuso el concepto de_x000D_
continuidad y tambi en un conocido teorema de la topolog a general que preserva la_x000D_
compacidad
Description
The continuity of a function de ned between classical topological spaces is a fundamental_x000D_
and very important for the development of mathematics and its applications_x000D_
topological concept. However, due to the complexity of the real world and the imprecision_x000D_
contained in many phenomena of nature these are described or better_x000D_
explained by fuzzy sets , which were introduced by the engineer L. Zadeh (1965) [7]._x000D_
The concept of fuzzy set generalizes the classical notion of set . A fuzzy set A in_x000D_
a universe X is associated with a function A : X ! [0; 1] that assigns to each_x000D_
element x of X a real number A(x) in [0; 1] called \ degree of membership " of the_x000D_
element x to the set A. A higher degree of membership re_x000D_
ects a sense of belonging_x000D_
to \ more " strong set A._x000D_
This work is based on the theory of fuzzy topological spaces introduced in 1968 by_x000D_
Chang [1] and is oriented to extend to the fuzzy context the concept of continuity_x000D_
and also a well-known theorem of general topology preserving compactness
Keywords
Espacios topológicos