Dendrites and light open mappings

Abstract:

It is shown that a metric continuum $X$ is a dendrite if and only if for every compact space $Y$ and for every light open mapping $f: Y \to f(Y)$ such that $X \subset f(Y)$ there is a copy $X’$ of $X$ in $Y$ for which the restriction $f|X’: X’ \to X$ is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also obtained.