Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A note on completely metrizable spaces
HTML articles powered by AMS MathViewer

by E. Michael PDF
Proc. Amer. Math. Soc. 96 (1986), 513-522 Request permission

Abstract:

Completely metrizable spaces are characterized by means of certain not necessarily open covers, and some applications are given to the preservation of complete metrizability under mappings.
References
    P. Alexandrov, Sur les ensembles de la première classe et les espaces abstraits, C. R. Acad. Sci. Paris Sér. I. Math. 178 (1924), 185-187.
  • A. V. Arhangel′skiĭ, On topological spaces which are complete in the sense of Čech, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1961 (1961), no. 2, 37–40 (Russian, with English summary). MR 0131258
  • J. Chaber, M. M. Čoban, and K. Nagami, On monotonic generalizations of Moore spaces, Čech complete spaces and $p$-spaces, Fund. Math. 84 (1974), no. 2, 107–119. MR 343244, DOI 10.4064/fm-84-2-107-119
  • Zdeněk Frolík, Generalizations of the $G_{\delta }$-property of complete metric spaces, Czechoslovak Math. J. 10(85) (1960), 359–379 (English, with Russian summary). MR 116305
  • N. Ghoussoub and B. Maurey, $G_\delta$-embeddings in Hilbert space, J. Funct. Anal. 61 (1985), no. 1, 72–97. MR 779739, DOI 10.1016/0022-1236(85)90039-4
  • F. Hausdorff, Die Mengen ${G_\delta }$ in vollständigen Räumen, Fund. Math. 6 (1924), 146-148. —, Über innere Abbildungen, Fund. Math. 23 (1934), 279-291.
  • K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
  • E. Michael, Complete spaces and tri-quotient maps, Illinois J. Math. 21 (1977), no. 3, 716–733. MR 467688
  • D. Montgomery, Non-separable metric spaces, Fund. Math. 25 (1935), 527-533. F. Topsøe, Topological games and Čech completeness, Proc. Fifth Prague Topological Symposium, 1981, Sigma Series in Pure Math., vol. 3, Heldermann, Berlin, 1982. pp. 613-630.
  • Howard H. Wicke, Open continuous images of certain kinds of $M$-spaces and completeness of mappings and spaces, General Topology and Appl. 1 (1971), no. 1, 85–100. MR 282348
  • N. Wedenissoff, Sur les espaces metriques complets, J. Math. Pures Appl. (9) 9 (1930), 377-381.
  • H. H. Wicke and J. M. Worrell Jr., On the open continuous images of paracompact Čech complete spaces, Pacific J. Math. 37 (1971), 265–275. MR 307173
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54E50, 54C10
  • Retrieve articles in all journals with MSC: 54E50, 54C10
Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 96 (1986), 513-522
  • MSC: Primary 54E50; Secondary 54C10
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0822451-6
  • MathSciNet review: 822451