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Monotone Classes of Dendrites
Published online by Cambridge University Press: 20 November 2018
Abstract
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Continua
$X$
and
$Y$
are monotone equivalent if there exist monotone onto maps
$f\,:\,X\,\to \,Y$
and
$g:\,Y\to \,X.\,\text{A}$
. A continuum
$X$
is isolated with respect to monotone maps if every continuumthat is monotone equivalent to
$X$
must also be homeomorphic to
$X$
. In this paper we show that a dendrite
$X$
is isolated with respect to monotone maps if and only if the set of ramification points of
$X$
is finite. In this way we fully characterize the classes of dendrites that are monotone isolated.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 2016
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