Sums and products of ultracomplete topological spaces

Abstract

In 1987 V.I. Ponomarev and V.V. Tkachuk characterized strongly complete topological spaces as those spaces which have countable character in their Stone–Čech compactification. On the other hand, in 1998 S. Romaguera introduced the notion of cofinally Čech complete spaces and he showed that a metrizable space admits a cofinally complete metric (otherwise, called ultracomplete metric), a term introduced independently by N.R. Howes in 1971 and A. Császár in 1975, if and only if it is cofinally Čech complete. In a recent paper the authors showed that these two notions are equivalent and in this way answered a question raised by Ponomarev and Tkachuk [Vestnik MGU 5 (1987) 16–19] about giving an internal characterization for strongly complete topological spaces (termed ultracomplete by the authors). In this paper, sums and products of ultracomplete spaces are studied.