## Abstract

We prove the following theorems: Theorem 1. Let X be an n-dimensional hereditarily indecomposable continuum. Then there exist l-dimensional hereditarily indecomposable continua Y_{1}, Y_{2},...) Y_{n} <nd monotone maps pi : X → Y_{1} such that (p1,p2,...,pn) X → KI × YI × ... × Y_{n} is an embedding and the space C(X) of all subcontinua of X is embeddable in C(Yi) × C(V2) × ... × C(Y_{n}) by K ∈ C(X) ∈ (pi(K),p2(K),...,Pn(K)). Theorem 2. For every open monotone map if with non-trivial sufficiently small fibers on a finite dimensional hereditarily indecomposable continuum X with dim X > 2 there exists α l-dimensional subcontinuum Y ⊂ X such that dim φ(Y) = ∞ and the restriction of fp to Y is also monotone and open. The connection between these theorems and other results in Hyperspace theory is studied.

Original language | English |
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Pages (from-to) | 603-609 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 125 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jan 1997 |

Externally published | Yes |

## Keywords

- Hereditarily indecomposable continua
- Hyperspaces
- Open monotone maps

## ASJC Scopus subject areas

- Mathematics (all)
- Applied Mathematics