# Fans are not c-determined

Colloquium Mathematicae (1999)

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

## Access Full Article

top## Abstract

top## How to cite

topIllanes, 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

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

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.