On metrizable type (MT-) maps and spaces (Q1304864)

The authors define paracompact, collectionwise normal, metrizable type (MT) and other types of maps, and prove their properties and relations similar to the classical ones for corresponding properties of spaces. From other results: (Corollary 5.14) A T\(_3\)-space having a \(G_\delta\)-diagonal is metrizable provided it is an MT-preimage of a metrizable space (thus, e.g., there is no MT-map mapping the Sorgenfrey line into a metrizable space -- Proposition 4.10).