Abstract:We show that a Tychonoff space is the perfect pre-image of a cofinally complete metric space if and only if it is paracompact and cofinally \v {C}ech complete. Further properties of these spaces are discussed. In particular, cofinal \v {C}ech completeness is preserved both by perfect mappings and by continuous open mappings.
Keywords: cofinally \v {C}ech complete, paracompact, cofinally complete metric space, perfect mapping
AMS Subject Classification: 54E50, 54C10, 54D20