induced mapping

Let $f: X \to Y$ be a mapping between continua. Then the induced mapping $C(f): C(X) \to C(Y)$ is defined by C(f)(A) = f(A), where A in the left member of the equality means an element of C(X), while in the right one it is understood as a subcontinuum of X (see [64, (0.49), p. 23]).