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Keywords:
cofinally \v {C}ech complete; paracompact; cofinally complete metric space; perfect mapping
cofinally \v {C}ech complete; paracompact; cofinally complete metric space; perfect mapping
Summary:
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.
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