Countable sums and products of metrizable spaces in ZF

We study the role that the axiom of choice plays in Tychonoff's product theorem restricted to countable families of compact, as well as, Lindelöf metric spaces, and in disjoint topological unions of countably many such spaces. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)