Geodesic
Monotone Classes of Dendrites
Canadian journal of mathematics, Tome 68 (2016) no. 3, pp. 675-697

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DOI

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.
DOI : 10.4153/CJM-2015-027-1
Mots-clés : 54F50, 54C10, 06A07, 54F15, 54F65, 03E15, dendrite, monotone, bqo, antichain 
Martínez-de-la-Vega, Veronica; Mouron, Christopher. Monotone Classes of Dendrites. Canadian journal of mathematics, Tome 68 (2016) no. 3, pp. 675-697. doi: 10.4153/CJM-2015-027-1
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     title = {Monotone {Classes} of {Dendrites}},
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     year = {2016},
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     doi = {10.4153/CJM-2015-027-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-027-1/}
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