C1(X) on the edge of C2(X)

• Autores: Javier Camargo, Sergio Macías, David Maya
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 1, 2025, págs. 341-368
• Idioma: inglés
• DOI: 10.4995/agt.2025.22003
• Enlaces
  • Texto completo
• Resumen

  • Given a continuum X and a positive integer n, let Cn(X) be the hyperspace consisting of all nonempty closed subsets of X having at most n components. For a subcontinuum A of X having empty interior, consider the following properties: A is a subcontinuum of colocal connectedness, X\A is continuumwise connected, A is a nonblock subcontinuum, A is a shore subcontinuum, A is not a strong centre. In this paper, we prove that C1(X) has all of these properties in Cn(X) if n ≥ 3, and we study when C1(X) has one of these properties in C2(X) .

• Referencias bibliográficas
  • J. G. Anaya y D. Maya, Non-cut ordered arcs of the hyperspace of subcontinua, Topology Appl. 349 (2024), 108908. https://doi.org/10.1016/j.topol.2024.108908
  • R. H. Bing, Embedding circle-like continua in the plane, Canadian J. Math. 14 (1962), 113-128. https://doi.org/10.4153/CJM-1962-009-3
  • J. Bobok, P. Pyrih y B. Vejnar, Non-cut shore and non-block points in continua, Glasnik Mat. Ser. III 51 (2016), 237-253. https://doi.org/10.3336/gm.51.1.14
  • J. Camargo, R. A. López y S. Macías, On weakly continuum-chainable and almost continuum-chainable continua, Topology Appl. 345 (2024), 108833....
  • J. Camargo y S. Macías, Quotients of n-fold hyperspaces, Topology Appl. 197 (2016), 154-166. https://doi.org/10.1016/j.topol.2015.10.001
  • J. Camargo y S. Macías, On Wilder, Strongly Wilder, Continuumwise Wilder, D, D*, y D** continua, Bull. Malays. Math. Sci. Soc. 47, (2024),...
  • J. Camargo y S. Macías, More on quotients of n-fold hyperspaces,Houston J. Math., 50 (2024), 443-475.
  • J. Camargo y S. Macías, More on T-closed sets, preprint.
  • J. Camargo, D. Maya y P. Pellicer-Covarrubias, Noncut subsets of the hyperspace of subcontinua, Topology Appl. 305 (2022), 107867. https://doi.org/10.1016/j.topol.2021.107867
  • B. Espinoza y E. Matsuhashi, D-continua, D*-continua, y Wilder continua, Topology Appl. 285 (2020), 107393. https://doi.org/10.1016/j.topol.2020.107393
  • G. Higuera y A. Illanes, Induced mappings on symmetric products, Topology Proc. 37 (2011), 367-401.
  • J. G. Hocking y G. S. Young, Topology, Dover Publications, Inc., New York, 1988.
  • A. Illanes, V. Martínez-de-la-Vega, J. M. Martínez-Montejano y D. Michalik, Diagonals separating the square of a continuum, Bull. Malays....
  • A. Illanes, V. Martínez-de-la-Vega, J. M. Martínez-Montejano y D. Michalik, Diagonals of the square of a continuum, Topology Appl. 364 (2025),...
  • S. Macías, Aposyndetic properties of symmetric products of continua, Topology Proc. 22 (1997), 281-296.
  • S. Macías, Topics on Continua, 2nd Edition, Springer-Cham, (2018). https://doi.org/10.1007/978-3-319-90902-8
  • S. Macías, The property of Kelley and continua, Rev. Integr. Temas Mat. 37, no. 1 (2019), 17-29. https://doi.org/10.18273/revint.v37n1-2019002
  • S. Macías, Set Function T: An Account on F. B. Jones' Contributions to Topology, Series Developments in Mathematics, vol. 67, Springer,...
  • V. Martínez-De-La-Vega y J. Martínez-Montejano, Concerning when F1(X) is a continuum of colocal connectedness in hyperspaces and symmetric...
  • J. Martínez-Montejano, Mutual aposyndesis of symmetric products, Topology Proc. 24 (1999), 203-213.
  • R. L. Moore, Foundations of point set theory, Colloquium Publications, vol. 13, American Mathematical Society, Providence, Rhode Island (1962).
  • S. B. Nadler, Jr., Hyperspaces of Sets: A Text with Research Questions, Monographs and Textbooks in Pure and Applied Mathematics, vol. 49,...
  • R. W. Wardle, On a property of J. L. Kelley, Houston J. Math. 3 (1977), 291-299.
  • G. T. Whyburn, Analytic topology, Colloquium Publications, vol. 28, American Mathematical Society, Providence, Rhode Island (1942). https://doi.org/10.1090/coll/028