Monotone maps of hereditarily indecomposable continua

Wayne Lewis

doi:10.1090/S0002-9939-1979-0532166-6

Monotone maps of hereditarily indecomposable continua

Wayne Lewis

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We prove that every hereditarily indecomposable continuum is the image under an open, monotone map of a one-dimensional hereditarily indecomposable continuum. Thus there exists a one-dimensional hereditarily indecomposable continuum with infinite dimensional hyperspace.

Original language	English
Pages (from-to)	361-364
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	75
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1979-0532166-6
State	Published - Jul 1979

Keywords

Continuum
Hyperspace
Indecomposable
Monotone

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10.1090/S0002-9939-1979-0532166-6

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title = "Monotone maps of hereditarily indecomposable continua",

abstract = "We prove that every hereditarily indecomposable continuum is the image under an open, monotone map of a one-dimensional hereditarily indecomposable continuum. Thus there exists a one-dimensional hereditarily indecomposable continuum with infinite dimensional hyperspace.",

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AB - We prove that every hereditarily indecomposable continuum is the image under an open, monotone map of a one-dimensional hereditarily indecomposable continuum. Thus there exists a one-dimensional hereditarily indecomposable continuum with infinite dimensional hyperspace.

KW - Continuum

KW - Hyperspace

KW - Indecomposable

KW - Monotone

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Monotone maps of hereditarily indecomposable continua

Abstract

Keywords

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