Monotone Classes of Dendrites

Continua X and Y are monotone equivalent if there exist monotone onto maps f : X→ Y and g: Y →X. 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.