Hyperspaces and open monotone maps of hereditarily indecomposable continua

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3 Scopus citations

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 Y1, Y2,...) Yn <nd monotone maps pi : X → Y1 such that (p1,p2,...,pn) X → KI × YI × ... × Yn is an embedding and the space C(X) of all subcontinua of X is embeddable in C(Yi) × C(V2) × ... × C(Yn) 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 languageEnglish
Pages (from-to)603-609
Number of pages7
JournalProceedings of the American Mathematical Society
Volume125
Issue number2
DOIs
StatePublished - 1 Jan 1997
Externally publishedYes

Keywords

  • Hereditarily indecomposable continua
  • Hyperspaces
  • Open monotone maps

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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