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cofinally \v {C}ech complete; paracompact; cofinally complete metric space; perfect mapping
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.
[1] Burdick B.S.: A note on completeness of hyperspaces. General Topology and Applications: Fifth Northeast Conference, eds: Susan Andima et al., Marcel Dekker, 1991, pp.19-24. MR 1142791 | Zbl 0766.54008
[2] Corson H.H.: The determination of paracompactness by uniformities. Amer. J. Math. 80 (1958), 185-190. MR 0094780 | Zbl 0080.15803
[3] Császár Á.: Strongly complete, supercomplete and ultracomplete spaces. Mathematical Structures-Computational Mathematics-Mathematical Modelling, Papers dedicated to Prof. L. Iliev's 60th Anniversary, Sofia, 1975, pp.195-202.
[4] Engelking R.: General Topology. Polish. Sci. Publ., Warsaw, 1977. MR 0500780 | Zbl 0684.54001
[5] Gruenhage G.: Generalized metric spaces. in Handbook of Set-Theoretic Topology, eds: K. Kunen and J. Vaughan, North-Holland, 1984, pp.425-501. MR 0776629 | Zbl 0794.54034
[6] Howes N.R.: Modern Analysis and Topology. Springer-Verlag, 1995. MR 1351251 | Zbl 0853.54002
[7] Isiwata T.: Mappings and spaces. Pacific J. Math. 20 (1967), 455-480. MR 0219044 | Zbl 0149.40501
[8] Kelley J.C.: General Topology. Van Nostrand, 1955. MR 0070144 | Zbl 0518.54001
[9] Künzi H.P.A., Romaguera S.: Quasi-metric spaces quasi-metric hyperspaces and uniform local compactness. Rend. Ist. Mat. Univ. Trieste, to appear. MR 1718967
[10] Rice M.D.: A note on uniform paracompactness. Proc. Amer. Math. Soc. 62 (1977), 359-362. MR 0436085 | Zbl 0353.54011
[11] Romaguera S.: On cofinally complete metric spaces. Questions Answers Gen. Topology 16 (1998), 165-170. MR 1642068 | Zbl 0941.54030
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