Artículo Original
Publicado 2005-12-12
Palabras clave
- hiperespacios de continuos,
- espacios métricos,
- espacios compactos y conexos
Cómo citar
Macías, S. (2005). Un breve panorama de los hiperespacios de continuos. Revista Integración, Temas De matemáticas, 23(2), 1–13. Recuperado a partir de https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/384
Resumen
El propósito de este artículo es presentar una pequeña introducción a los hiperespacios más estudiados de continuos (i.e., de espacios métricos, compactos y conexos).
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Referencias
[1] K. Borsuk and S. Ulam. “On symmetric products of topological spaces”, Bull. Amer. Math. Soc., 37 (1931), 875–882.
[2] J. J. Charatonik, A. Illanes and S. Macías. “Induced mappings on the hyperspaces Cn(X) of a continuum X”, Houston J. Math., 28 (2002), 781–805.
[3] D. Curtis and N. T. Nhu. “Hyperspaces of finite subsets which are homeomorphic to ℵ0–dimensional linear metric spaces”, Topology Appl., 19 (1985), 251–260.
[4] J. Grispolakis and E. D. Tymchatyn. “Irreducible continua with nondegenerate end–tranches and arcwise accessibility in hyperspaces”, Fund. Math., 100 (1980), 117–130.
[5]A. Illanes. “A model for the hyperspace C2 ¡ S 1 ¢ ”, Q & A in General Topology, 22 (2004), 117–130.
[6] A. Illanes, S. Macías and S. B. Nadler. “Symmetric products and Q–manifolds”, Geometry and Topology in Dynamics, Contemporary Math. Series of Amer. Math. Soc., Vol. 246, 1999, Providence, RI, 137–141.
[7] A. Illanes and S. B. Nadler, Jr. Hyperspaces: Fundamental and Recent Advances, Monographs and Textbooks in Pure and Applied Math., Vol. 216, Marcel Dekker, New York, Basel, 1999.
[8] J. L. Kelley. “Hyperspaces of a continuum”, Trans. Amer. Math. Soc., 52 (1942), 22–36.
[9] S. Macías. “Hiperespacios y productos simétricos de continuos”, Aportaciones Matemáticas, Serie Comunicaciones #27, Sociedad Matemática Mexicana, (2000), 211–223.
[10] S. Macías. “On symmetric products of continua”, Topology Appl., 92 (1999), 173–182.
[11] S. Macías. “Aposyndetic properties of symmetric products of continua”, Topology Proc., 22 (1997), 281–296.
[12] S. Macías. “Hereditarily indecomposable continua have unique hyperspace 2X”, Bol. Soc. Mat. Mexicana (3) 5 (1999), 415–418.
[13] S. Macías. “On the hyperspaces Cn(X) of a continuum X”, Topology Appl.,109 (2001), 237–256.
[14] S. Macías. “On the Hyperspaces Cn(X) of a continuum X”, II, Topology Proc., 25 (2000), 255–276.
[15] S. Macías. “On arcwise accessibility in hyperspaces”, Topology Proc., 26 (2001–2002), 247–254.
[16] S. Macías. “Connectedness of the hyperspace of closed subsets with at most n components”, Q & A in General Topology, 19 (2001), 133–138.
[17] S. Macías. “Fans whose hyperspaces are cones”, Topology Proc., 27 (2003), 217–222.
[18] S. Macías. Topics on Continua, Pure and Applied Mathematics Series, Vol. 275, Chapman & Hall/CRC, Taylor & Francis Group, Boca Raton, London, New York,Singapore, 2005.
[19] S. Macías and S. B. Nadler, Jr. “n–fold hyperspaces, cones and products”, Topology Proc., 26 (2001–2002), 255–270.
[20] S. Macías and S. B. Nadler, Jr. “Smoothness in n–fold hyperspaces”, Glasnik Mat., 37(57) (2002), 365–373.
[21] S. Macías and S. B. Nadler, Jr. “Z–Sets in hyperspaces”, Q & A in General Topology, 19 (2001), 227–241
.
[22] R. Molski. “On symmetric products”, Fund. Math., 44 (1957), 165–170.
[23] S. B. Nadler, Jr. “Arcwise accessibility in hyperspaces”, Dissertationes Math. (Rozprawy Mat.) 138 (1976), 1–29.
[24] S. B. Nadler, Jr. Hyperspaces of Sets: A Text with Research Questions, Monographs and Textbooks in Pure and Applied Math., Vol. 49, Marcel Dekker, NewYork, Basel, 1978.
[25] S. B. Nadler, Jr. Continuum Theory: An Introduction, Monographs and Textbooks in Pure and Applied Math., Vol. 158, Marcel Dekker, New York, Basel, Hong Kong, 1992.
[26] M. Wojdisławski. “Rétractes absolus et hyperespaces des continus”, Fund. Math., 32 (1939), 184–192
[2] J. J. Charatonik, A. Illanes and S. Macías. “Induced mappings on the hyperspaces Cn(X) of a continuum X”, Houston J. Math., 28 (2002), 781–805.
[3] D. Curtis and N. T. Nhu. “Hyperspaces of finite subsets which are homeomorphic to ℵ0–dimensional linear metric spaces”, Topology Appl., 19 (1985), 251–260.
[4] J. Grispolakis and E. D. Tymchatyn. “Irreducible continua with nondegenerate end–tranches and arcwise accessibility in hyperspaces”, Fund. Math., 100 (1980), 117–130.
[5]A. Illanes. “A model for the hyperspace C2 ¡ S 1 ¢ ”, Q & A in General Topology, 22 (2004), 117–130.
[6] A. Illanes, S. Macías and S. B. Nadler. “Symmetric products and Q–manifolds”, Geometry and Topology in Dynamics, Contemporary Math. Series of Amer. Math. Soc., Vol. 246, 1999, Providence, RI, 137–141.
[7] A. Illanes and S. B. Nadler, Jr. Hyperspaces: Fundamental and Recent Advances, Monographs and Textbooks in Pure and Applied Math., Vol. 216, Marcel Dekker, New York, Basel, 1999.
[8] J. L. Kelley. “Hyperspaces of a continuum”, Trans. Amer. Math. Soc., 52 (1942), 22–36.
[9] S. Macías. “Hiperespacios y productos simétricos de continuos”, Aportaciones Matemáticas, Serie Comunicaciones #27, Sociedad Matemática Mexicana, (2000), 211–223.
[10] S. Macías. “On symmetric products of continua”, Topology Appl., 92 (1999), 173–182.
[11] S. Macías. “Aposyndetic properties of symmetric products of continua”, Topology Proc., 22 (1997), 281–296.
[12] S. Macías. “Hereditarily indecomposable continua have unique hyperspace 2X”, Bol. Soc. Mat. Mexicana (3) 5 (1999), 415–418.
[13] S. Macías. “On the hyperspaces Cn(X) of a continuum X”, Topology Appl.,109 (2001), 237–256.
[14] S. Macías. “On the Hyperspaces Cn(X) of a continuum X”, II, Topology Proc., 25 (2000), 255–276.
[15] S. Macías. “On arcwise accessibility in hyperspaces”, Topology Proc., 26 (2001–2002), 247–254.
[16] S. Macías. “Connectedness of the hyperspace of closed subsets with at most n components”, Q & A in General Topology, 19 (2001), 133–138.
[17] S. Macías. “Fans whose hyperspaces are cones”, Topology Proc., 27 (2003), 217–222.
[18] S. Macías. Topics on Continua, Pure and Applied Mathematics Series, Vol. 275, Chapman & Hall/CRC, Taylor & Francis Group, Boca Raton, London, New York,Singapore, 2005.
[19] S. Macías and S. B. Nadler, Jr. “n–fold hyperspaces, cones and products”, Topology Proc., 26 (2001–2002), 255–270.
[20] S. Macías and S. B. Nadler, Jr. “Smoothness in n–fold hyperspaces”, Glasnik Mat., 37(57) (2002), 365–373.
[21] S. Macías and S. B. Nadler, Jr. “Z–Sets in hyperspaces”, Q & A in General Topology, 19 (2001), 227–241
.
[22] R. Molski. “On symmetric products”, Fund. Math., 44 (1957), 165–170.
[23] S. B. Nadler, Jr. “Arcwise accessibility in hyperspaces”, Dissertationes Math. (Rozprawy Mat.) 138 (1976), 1–29.
[24] S. B. Nadler, Jr. Hyperspaces of Sets: A Text with Research Questions, Monographs and Textbooks in Pure and Applied Math., Vol. 49, Marcel Dekker, NewYork, Basel, 1978.
[25] S. B. Nadler, Jr. Continuum Theory: An Introduction, Monographs and Textbooks in Pure and Applied Math., Vol. 158, Marcel Dekker, New York, Basel, Hong Kong, 1992.
[26] M. Wojdisławski. “Rétractes absolus et hyperespaces des continus”, Fund. Math., 32 (1939), 184–192