Fans are not c-determined

Alejandro Illanes

Colloquium Mathematicae (1999)

  • Volume: 81, Issue: 2, page 299-308
  • ISSN: 0010-1354

Abstract

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A continuum is a compact connected metric space. For a continuum X, let C(X) denote the hyperspace of subcontinua of X. In this paper we construct two nonhomeomorphic fans (dendroids with only one ramification point) X and Y such that C(X) and C(Y) are homeomorphic. This answers a question by Sam B. Nadler, Jr.

How to cite

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Illanes, Alejandro. "Fans are not c-determined." Colloquium Mathematicae 81.2 (1999): 299-308. <http://eudml.org/doc/210742>.

@article{Illanes1999,
abstract = {A continuum is a compact connected metric space. For a continuum X, let C(X) denote the hyperspace of subcontinua of X. In this paper we construct two nonhomeomorphic fans (dendroids with only one ramification point) X and Y such that C(X) and C(Y) are homeomorphic. This answers a question by Sam B. Nadler, Jr.},
author = {Illanes, Alejandro},
journal = {Colloquium Mathematicae},
keywords = {C-determined; hyperspaces; fan; continuum},
language = {eng},
number = {2},
pages = {299-308},
title = {Fans are not c-determined},
url = {http://eudml.org/doc/210742},
volume = {81},
year = {1999},
}

TY - JOUR
AU - Illanes, Alejandro
TI - Fans are not c-determined
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 2
SP - 299
EP - 308
AB - A continuum is a compact connected metric space. For a continuum X, let C(X) denote the hyperspace of subcontinua of X. In this paper we construct two nonhomeomorphic fans (dendroids with only one ramification point) X and Y such that C(X) and C(Y) are homeomorphic. This answers a question by Sam B. Nadler, Jr.
LA - eng
KW - C-determined; hyperspaces; fan; continuum
UR - http://eudml.org/doc/210742
ER -

References

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  1. [1] G. Acosta, Hyperspaces with unique hyperspace, preprint. Zbl1046.54024
  2. [2] R. D. Anderson, Topological properties of the Hilbert cube and the infinite product of open intervals, Trans. Amer. Math. Soc. 126 (1967), 200-216. Zbl0152.12601
  3. [3] R. Duda, On the hyperspace of subcontinua of a finite graph, I, Fund. Math. 69 (1968), 265-286. Zbl0167.51401
  4. [4] C. Eberhart and S. B. Nadler, Jr., Hyperspaces of cones and fans, Proc. Amer. Math. Soc. 77 (1979), 279-288. Zbl0413.57010
  5. [5] A. Illanes, Chainable continua are not C-determined, Topology Appl., to appear. Zbl0964.54004
  6. [6] J. Krasinkiewicz, On the hyperspaces of snake-like and circle-like continua, Fund. Math. 83 (1974), 155-164. Zbl0271.54024
  7. [7] S. Macías, On C-determined continua, Glas. Mat., to appear. 
  8. [8] S. Macías, Hereditarily indecomposable continua have unique hyperspace 2 X , preprint. Zbl0938.54010
  9. [9] S. B. Nadler, Jr., Hyperspaces of Sets, Monographs Textbooks Pure Appl. Math. 49, Marcel Dekker, New York, 1978. 
  10. [10] L. E. Ward, Extending Whitney maps, Pacific J. Math. 93 (1981), 465-469. Zbl0457.54008

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