Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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.




Extension of a result of Dieudonné

Authors: J. M. Worrell and H. H. Wicke
Journal: Proc. Amer. Math. Soc. 25 (1970), 634-637
MSC: Primary 54.30
MathSciNet review: 0264605
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Dieudonné showed that there exists a normal (countably) compact uniform ${T_1}$-space which has no topology preserving complete uniformity [4]. His example, being the space of the countable ordinals with respect to the order topology, everywhere locally has a complete uniformity. Here we show, as a corollary to Dieudonné’s result and a result of Worrell [10], that there exists a normal (countably) compact first countable involutorily homogeneous uniform ${T_1}$-space locally homeomorphic with itself which has no topology preserving complete uniformity.

References [Enhancements On Off] (What's this?)

  • A. V. Arhangel′skiĭ, Some metrization theorems, Uspehi Mat. Nauk 18 (1963), no. 5 (113), 139–145 (Russian). MR 0156318
  • R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), 175–186. MR 43449, DOI
  • D. van Dantzig, Ueber topologisch homogene Kontinua. Fund. Math. 15 (1930), 102-125.
  • Jean Dieudonné, Un exemple d’espace normal non susceptible d’une structure uniforme d’espace complet, C. R. Acad. Sci. Paris 209 (1939), 145–147 (French). MR 175
  • M. Fréchet, Sur quelques points du calcul fonctionnel, Rend. Circ. Math. Palermo 22 (1906), 1-74.
  • John L. Kelley, General topology, D. Van Nostrand Company, Inc., Toronto-New York-London, 1955. MR 0070144
  • R. L. Moore, Foundations of point set theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR 0150722
  • Howard H. Wicke, The regular open continuous images of complete metric spaces, Pacific J. Math. 23 (1967), 621–625. MR 219035
  • H. H. Wicke and J. M. Worrell Jr., Open continuous mappings of spaces having bases of countable order, Duke Math. J. 34 (1967), 255–271. MR 210084
  • J. M. Worrell, Jr., On compact spaces and Čech completeness, Notices Amer. Math. Soc. 13 (1966), 644. Abstract #66T-411.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.30

Retrieve articles in all journals with MSC: 54.30

Additional Information

Keywords: Complete uniformity, [ill]ech completeness, involutory homogeneity, arc, base of countable order, open mappings, (countably) compact, bicompact, normality, <IMG WIDTH="18" HEIGHT="21" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\aleph$">-wise Lindel&#246;fian, nowhere locally complete, fixed point
Article copyright: © Copyright 1970 American Mathematical Society