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-Cech compactification. On the other hand, in 1998 S. Romaguera intro- duced the notion of cofinally Cech complete spaces and he showed that a metriz- able space admits a cofinally complete metric (otherwise called ultracomplete metric), a term introduced independently by N.R. Howes in 1971 and A. Csaaszar in 1975, if and only if it is cofinally Cech complete. In this paper we show that these two notions are equivalent and in this way answer a question raised in [16] about giving an internal characterization for strongly complete topological spaces.