Geodesic
Perfect pre-images of cofinally complete metric spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 335-342.

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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.
Classification : 54C10, 54D20, 54E50
Keywords: cofinally \v {C}ech complete; paracompact; cofinally complete metric space; perfect mapping 
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     title = {Perfect pre-images of cofinally complete metric spaces},
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García-Máynez, A.; Romaguera, S. Perfect pre-images of cofinally complete metric spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 2, pp. 335-342. http://geodesic.mathdoc.fr/item/CMUC_1999__40_2_a15/