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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0264605-4
MathSciNet review:
0264605
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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.
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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 Lindelöfian,
nowhere locally complete,
fixed point
Article copyright:
© Copyright 1970
American Mathematical Society