Published 2022-09-20
Keywords
- Aposyndesis,
- Cantor manifold,
- Continuum,
- Colocal connectedness,
- (n, m)−fold hyperspace suspension
- Property (b),
- Unicoherent ...More
How to Cite
Copyright (c) 2022 Revista Integración, temas de matemáticas
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
Let n, m ∈ N with m ≤ n and X be a metric continuum. We consider the hyperspaces Cn(X) (respectively, Fn(X)) of all nonempty closed subsets of X with at most n components (respectively, n points). The (n, m)−fold hyperspace suspension on X was introduced in 2018 by Anaya, Maya, and Vázquez-Juárez, to be the quotient space Cn(X)/Fm(X) which is obtained from Cn(X) by identifying Fm(X) into a one-point set. In this paper we prove that Cn(X)/Fm(X) contains an n−cell; Cn(X)/Fm(X) has property (b); Cn(X)/Fm(X) is unicoherent; Cn(X)/Fm(X) is colocally connected; Cn(X)/Fm(X) is aposyndetic; and Cn(X)/Fm(X) is finitely aposyndetic
Downloads
References
- Anaya J.G., Maya D., and Vázquez-Juárez F., “The hyperspace HSn m(X) for a finite graph X is unique”, Topology Appl., 157 (2018), 428–439.
- Bennett D.E., “Aposyndetic properties of unicoherent continua”, Pacific J. Math., 37 (1971), no. 3, 585–589.
- Curtis D.W., and Nhu N.T., “Hyperspaces of finite subsets which are homeomorphic to ℵ0−dimensional linear metric spaces”, Topology Appl., 19 (1985), 251–260.
- Dugundji J., Topology, 2nd ed., BCS Associates, Moscow, Idaho, USA, 1978.
- Escobedo R., López M. de J., and Macías S., “On the hyperspace suspension of a continuum”, Topology Appl., 138 (2004), 109–124.
- Hernández-Valdez G., Herrera-Carrasco D., López M. de J., and Macías-Romero F.,“Uniqueness of the (n, m)−fold hyperspace suspension for continua”, sent to Topology Appl.
- Herrera-Carrasco D., “Dendrites with unique hyperspace”, Houston J. Math., 33 (2007), no. 3, 795–805.
- Herrera-Carrasco D., Illanes A., Macías-Romero F., and Vázquez-Juárez F., “Finite graphs have unique hyperspace HSn(X)”, Topology Proc., 44 (2014), 75–95.
- Herrera-Carrasco D., López M. de J., and Macías-Romero F., “Framed continua have unique n−fold hyperspace suspension”, Topology Appl., 196 (2015), 652–667.
- Herrera-Carrasco D., López M. de J., and Macías-Romero F., “Almost meshed locally connected continua without unique n−fold hyperspace suspension”, Houston J. Math., 44 (2018), no. 4, 1335–1365.
- Illanes A. and Nadler, Jr., S.B., Hyperspaces Fundamentals and Recent Advances, Monographs and Textbooks in Pure and Applied Math., vol. 216, Marcel Dekker, Inc., New York, 1999.
- Kuratowski K., Topology, Vol. II, Academic Press, New York, 1968.
- Levin M., and Sternfeld Y., “The space of subcontinua of a 2–dimensional continuum is infinitely dimensional”, Proc. Amer. Math. Soc., 125 (1997), 2771–2775.
- Libreros-López A., Macías-Romero F., and Herrera-Carrasco D., “On the uniqueness of n−fold pseudo-hyperspace suspension for locally connected continua”, Topology Appl., 312 (2022), 108053, 22 pp.
- Macías J.C., “On the n−fold pseudo-hyperspace suspensions of continua”, Glas. Mat. Ser. III, 43 (2008), 439–449.
- Macías S., “On the hyperspaces Cn(X) of a continuum X”, Topology Appl., 109 (2001), 237–256.
- Macías S., “On the n−fold hyperspace suspension of continua”, Topology Appl., 138 (2004), 125–138.
- Macías S., “On the n−fold hyperspace suspension of continua, II”, Glas. Mat. Ser. III, 41 (2006), no. 61, 335–343.
- Macías S., Topics on continua, 2nd ed., Springer, Cham, Switzerland, 2018.
- Macías S., and Nadler, Jr. S.B., “n−fold hyperspace, cones, and products”, Topology Proc., 26 (2001–2002), 255–270.
- Montero-Rodríguez G., Herrera-Carrasco D., López M. de J., and Macías-Romero F., “Finite graphs have unique n−fold symmetric product suspension”, Houston J. Math., 47 (2021), no. 4, 20 pp.
- Morales-Fuentes U., “Finite graphs have unique n−fold pseudo-hyperspace suspension”, Topology Proc., 52 (2018), 219–233.
- Nadler, Jr., S.B., Hyperspaces of sets, Monographs and Textbooks in Pure and Applied Math. vol. 49, Marcel Dekker, Inc., New York, 1978.
- Nadler, Jr., S.B., “A fixed point theorem for hyperspace suspensions”, Houston J. Math., 5 (1979), 125–132.
- Nadler, Jr., S.B., Continuum Theory: An Introduction, Monographs and Textbooks in Pure and Applied Math., vol. 158, Marcel Dekker, Inc., New York, 1992.
- Nadler, Jr., S.B., Dimension Theory: An introduction with exercises, Aportaciones Matemáticas Serie Textos 18, Sociedad Matemática Mexicana, Mexico, 2002.
- Whyburn G.T., Analytic Topology, Amer. Math. Soc. Colloq. Publ., vol. 28, American Mathematical Society, Providence, RI, 1942.