Continuos g-contraíbles

MICHAEL A. RINCÓN-VILLAMIZAR^*
Universidad Industrial de Santander, Escuela de Matemáticas, Bucaramanga, Colombia.

Resumen. Diremos que un continuo X es g-contraíble si existe una función continua y sobreyectiva ƒ : X → X que es homotópica a una función constante. En este artículo hacemos una recopilación de los resultados conocidos acerca de los continuos g-contraíbles.Mostraremos que existe un continuo que no es g-contraíble tal que el producto numerable de él con sí mismo sí lo es. Con esto damos respuesta negativa a un caso particular de la Pregunta 3.2 que propusimos en el artículo "On g-contractibility of continua" [3].

Palabras Claves: continuo, contraíble, g-contraíble, cono, homotopía, uniformemente conexo por caminos, dendroide.
MSC2010: 54F15, 54G20, 54C05.

g-contractible continua

Abstract. A continuum X is said to be g-contractible provided that there is a surjective map ƒ : X → X which is homotopic to a constant map. In this article, we will study g-contractible continua. Answering a particular case of a proposed question in the article "On g-contractibility of continua" [3], we will show that there exists a non-g-contractible continuum X such that its countable product X^ℕ is g-contractible.

Keywords: continua, contractible, g-contractible, cone, homotopy, uniformly path connected, dendroid.

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Referencias

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^*E-mail : mrincon81@gmail.com
Recibido: 23 de abril de 2012, Aceptado: 4 de junio de 2012.