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Search: MSC category 54F50 ( Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03] )

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Martínez-de-la-Vega, Veronica; Mouron, Christopher
Monotone Classes of Dendrites
Continua $X$ and $Y$ are monotone equivalent if there exist monotone onto maps $f:X\longrightarrow Y$ and $g:Y\longrightarrow X$. A continuum $X$ is isolated with respect to monotone maps if every continuum that 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.

Keywords:dendrite, monotone, bqo, antichain
Categories:54F50, 54C10, 06A07, 54F15, 54F65, 03E15

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