A NOTE ON LIGHT INDUCED MAPPINGS

Abstract

Let a mapping $f:X\to Y$ between continua $X$ and $Y$ be given. We shall prove: a) if the induced mapping $2^f:2^X\to 2^Y$ is light, then $w\left(X\right)=w\left(Y\right)$. In particular, if $Y$ is metrizable, then $X$ is metrizable, b) if the induced mapping $C\left(f\right):C\left(X\right)\to C\left(Y\right)$ is light and $X$ is a $\mathrm{D}$-continuum, then $w\left(X\right)=w\left(Y\right)$.