Light maps and extensional dimension (Q1371928)

The authors prove that light maps \(f: X\to Y\) between compacta admit decompositions of the type \(f=g \circ h\), where \(g:Z\to Y\) is a finite-to-one map of a special type and \(h: X\to Z\) has arbitrarily small point-inverses. Therefore light maps between compacta cannot lower extensional dimension. A generalization of the classical Hurewicz theorem on dimension-raising maps to the case of extensional dimension is also obtained.