Induced almost continuous functions on hyperspaces

Abstract

For a metric continuum $X$, let $C(X)$ (resp., $2^{X}$) be the hyperspace of subcontinua (resp., nonempty closed subsets) of $X$. Let $f:X\rightarrow Y$ be an almost continuous function. Let $C(f):C(X)\rightarrow C(Y)$ and $ 2^{f}:2^{X}\rightarrow 2^{Y}$