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Revista Integración
Print version ISSN 0120-419X
Integración - UIS vol.30 no.1 Bucaramanga Jan./June 2012
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 Xℕ is g-contractible.
Keywords: continua, contractible, g-contractible, cone, homotopy, uniformly path connected, dendroid.
Texto Completo disponible en PDF
Referencias
[1] Bellamy D.P., The cone over the Cantor set-continuous maps from both directions, Topology Conference (Proc. General Topology Conf., Emory Univ., Atlanta, Ga., 1970), 825, Dept. Math., Emory Univ., Atlanta, Ga., 1970. [ Links ]
[2] Bellamy D.P. and Hagopian C.L., "Mapping continua onto their cones", Colloq. Math. 41 (1979), no. 1, 5356. [ Links ]
[3] Camargo J., Pellicer-Covarrubias P. and Rincón-Villamizar M.A., "On g-contractibility of continua", preprint. [ Links ]
[4] Charatonik J.J., "Two invariants under continuity and the comparability of fans", Fund. Math. 53 (1964), 187204. [ Links ]
[5] Charatonik J.J., "On ramification points in the classical sense", Fund. Math. 51 (1962), 229252. [ Links ]
[6] Dugundji J., Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. [ Links ]
[7] Engelking R. and Lelek A., "Cartesian products and continuous images", Colloq. Math. 8 (1961), 2729. [ Links ]
[8] Illanes A., "A continuum whose hyperspace of subcontinua is not g-contractible", Proc. Amer. Math. Soc. 130 (2002), no. 7, 21792182. [ Links ]
[9] Illanes A. and Nadler S.B., Jr., Hyperspaces. Fundamentals and recent advances, Monographs and Textbooks in Pure and Applied Mathematics, 216. Marcel Dekker, Inc., New York, 1999. [ Links ]
[10] Kuperberg W., "Uniformly pathwise connected continua", Studies in topology, (Proc. Conf., Univ. North Carolina, Charlotte, NC), (1975), 315324. [ Links ]
[11] Krezeminska I. and Prajs J.R., "A non-g-contractible uniformly path connected continuum", Topology Appl. 91 (1999), no. 2, 151158. [ Links ]
[12] Munkres J.R., Topology, 2nd ed., Prentice-Hall, Inc., Upper Saddle River, NJ, 2000. [ Links ]
[13] Nadler S.B., Jr., Continuum theory. An introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158. Marcel Dekker, Inc., New York, 1992. [ Links ]
[14] Nadler S.B., Jr., Hyperspaces of sets. A text with research questions, Monographs and Textbooks in Pure and Applied Mathematics, 49, Marcel Dekker, Inc., New York, 1978. [ Links ]
[15] Patty C.W., Foundations of Topology, Second edition, Jones and Bartlett Publishers, Boston, MA, 2009. [ Links ]
*E-mail : mrincon81@gmail.com
Recibido: 23 de abril de 2012, Aceptado: 4 de junio de 2012.