# Hyperspaces of two-dimensional continua

Fundamenta Mathematicae (1996)

- Volume: 150, Issue: 1, page 17-24
- ISSN: 0016-2736

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topLevin, Michael, and Sternfeld, Yaki. "Hyperspaces of two-dimensional continua." Fundamenta Mathematicae 150.1 (1996): 17-24. <http://eudml.org/doc/212159>.

@article{Levin1996,

abstract = {Let X be a compact metric space and let C(X) denote the space of subcontinua of X with the Hausdorff metric. It is proved that every two-dimensional continuum X contains, for every n ≥ 1, a one-dimensional subcontinuum $T_n$ with $dim C (T_n) ≥ n$. This implies that X contains a compact one-dimensional subset T with dim C (T) = ∞.},

author = {Levin, Michael, Sternfeld, Yaki},

journal = {Fundamenta Mathematicae},

keywords = {hyperspaces; hereditarily indecomposable continua; one- and two-dimensional continua; hereditarily indecomposable continuum},

language = {eng},

number = {1},

pages = {17-24},

title = {Hyperspaces of two-dimensional continua},

url = {http://eudml.org/doc/212159},

volume = {150},

year = {1996},

}

TY - JOUR

AU - Levin, Michael

AU - Sternfeld, Yaki

TI - Hyperspaces of two-dimensional continua

JO - Fundamenta Mathematicae

PY - 1996

VL - 150

IS - 1

SP - 17

EP - 24

AB - Let X be a compact metric space and let C(X) denote the space of subcontinua of X with the Hausdorff metric. It is proved that every two-dimensional continuum X contains, for every n ≥ 1, a one-dimensional subcontinuum $T_n$ with $dim C (T_n) ≥ n$. This implies that X contains a compact one-dimensional subset T with dim C (T) = ∞.

LA - eng

KW - hyperspaces; hereditarily indecomposable continua; one- and two-dimensional continua; hereditarily indecomposable continuum

UR - http://eudml.org/doc/212159

ER -

## References

top- [1] R. H. Bing, Higher-dimensional hereditarily indecomposable continua, Trans. Amer. Math. Soc. 71 (1951), 267-273. Zbl0043.16901
- [2] A. Lelek, On mappings that change dimension of spheres, Colloq. Math. 10 (1963), 45-48. Zbl0113.16601
- [3] M. Levin, Hyperspaces and open monotone maps of hereditarily indecomposable continua, Proc. Amer. Math. Soc., to appear. Zbl0862.54011
- [4] M. Levin and Y. Sternfeld, Mappings which are stable with respect to the property dim f(X)≥ k, Topology Appl. 52 (1993), 241-265.
- [5] M. Levin and Y. Sternfeld, The space of subcontinua of a 2-dimensional continuum is infinite dimensional, Proc. Amer. Math. Soc., to appear. Zbl0891.54004
- [6] S. B. Nadler Jr., Hyperspaces of Sets, Dekker, 1978.
- [7] Y. Sternfeld, Mappings in dendrites and dimension, Houston J. Math. 19 (1993), 483-497. Zbl0819.54024

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