Rocky Mountain Journal of Mathematics

Uniqueness of hyperspaces for Peano continua

Rodrigo Hernández-Gutiérrez, Alejandro Illanes, and Verónica Martínez-De-La-Vega

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 43, Number 5 (2013), 1583-1624.

Dates
First available in Project Euclid: 25 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1382705670

Digital Object Identifier
doi:10.1216/RMJ-2013-43-5-1583

Mathematical Reviews number (MathSciNet)
MR3127839

Zentralblatt MATH identifier
1280.54018

Keywords
Almost meshed continuum dendrite hyperspace local dendrite meshed unique hyperspace Peano continuum

Citation

Hernández-Gutiérrez, Rodrigo; Illanes, Alejandro; Martínez-De-La-Vega, Verónica. Uniqueness of hyperspaces for Peano continua. Rocky Mountain J. Math. 43 (2013), no. 5, 1583--1624. doi:10.1216/RMJ-2013-43-5-1583. https://projecteuclid.org/euclid.rmjm/1382705670


Export citation

References

  • G. Acosta, Continua with unique hyperspace, in Continuum theory, Lect. Notes Pure Appl. Math. 230 (2002), 33-49.
  • G. Acosta and D. Herrera-Carrasco, Dendrites without unique hyperspace, Houston J. Math. 35 (2009), 451-467.
  • G. Acosta, D. Herrera-Carrasco and F. Macías-Romero, Local dendrites with unique hyperspace $C(X)$, Topol. Appl. 157 (2010), 2069-2085.
  • R.D. Anderson, Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math Soc. 126 (1967), 200-216.
  • D. Arévalo, W.J. Charatonik, P. Pellicer-Covarrubias and L. Simón, Dendrites with a closed set of end points, Topol. Appl. 115 (2001), 1-17.
  • R.H. Bing, Partitioning a set, Bull. Amer. Math. Soc. 55 (1949), 1101-1110.
  • J.J. Charatonik and A. Illanes, Local connectedness in hyperspaces, Rocky Mountain J. Math. 36 (2006), 811-856.
  • D.W. Curtis, Growth hyperspaces of Peano continua, Trans. Amer. Math. Soc. 238 (1978), 271-283.
  • D.W. Curtis and R.M. Schori, $2^{X}$ and $C(X)$ are homeomorphic to the Hilbert cube, Bull. Amer. Math. Soc. 80 (1974), 927-931.
  • –––, Hyperspaces of Peano continua are Hilbert cubes, Fund. Math. 101 (1978), 19-38.
  • R. Duda, On the hyperspace of subcontinua of a finite graph, I, Fund. Math. 62 (1968), 265-286.
  • –––, Correction to the paper On the hyperspace of subcontinua of a finite graph I, Fund. Math. 69 (1970), 207-211.
  • D. Herrera-Carrasco, Dendrites with unique hyperspace, Houston J. Math. 33 (2007), 795-805.
  • D. Herrera-Carrasco, A. Illanes, M.J. López and F. Macías-Romero, Dendrites with unique hyperspace $C_{2}(X)$, Topol. Appl. 156 (2009), 549-557.
  • D. Herrera-Carrasco and F. Macías-Romero, Dendrites with unique $n$-fold hyperspace, Topol. Proc. 32 (2008), 321-337.
  • A. Illanes, The hyperspace $C_{2}(X)$ for a finite graph $X$ is unique, Glas. Mat. Ser. 37 (2002), 347-363.
  • –––, Finite graphs $X$ have unique hyperspaces $C_{n}(X)$, Topol. Proc. 27 (2003), 179-188.
  • –––, Dendrites with unique hyperspace $ C_{2}(X)$ II, Topol. Proc. 34 (2009), 77-96.
  • A. Illanes and S.B. Nadler, Jr., Hyperspace fundamentals and recent advances, Mono. Text. Pure Appl. Math. 216, Marcel Dekker, New York, 1999.
  • S. Macías, On the hyperspaces $C_{n}(X)$ of a continuum $X$, Topol. Appl. 109 (2001), 237-256.
  • V. Martínez-de-la-Vega, Dimension of the $n$-fold hyperspaces of graphs, Houston J. Math. 32 (2006), 783-799.
  • E.E. Moise, Grille decomposition and convexification theorems for compact metric locally connected continua, Bull. Amer. Math. Soc. 55 (1949), 1111-1121.
  • S.B. Nadler, Jr., Continuum theory, An introduction, Mono. Text. Pure Appl. Math. 158, Marcel Dekker, New York, 1992.
  • H. Toruńczyk, On $CE$-images of the Hilbert cube and characterization of $Q$-manifolds, Fund. Math. 106 (1980), 31-40. \noindentstyle