The inverse image of a metric space under a biquotient compact mapping
C. M. Pareek (1972)
Compositio Mathematica
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C. M. Pareek (1972)
Compositio Mathematica
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Nagata, J.
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Alexandroff, P.
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Adalberto García-Máynez, Salvador Romaguera (1999)
Commentationes Mathematicae Universitatis Carolinae
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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 Čech complete. Further properties of these spaces are discussed. In particular, cofinal Čech completeness is preserved both by perfect mappings and by continuous open mappings.