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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: 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

DOI: https://doi.org/10.1090/S0002-9939-1970-0264605-4
Keywords: Complete uniformity, [ill]ech completeness, involutory homogeneity, arc, base of countable order, open mappings, (countably) compact, bicompact, normality, $ \aleph $-wise Lindelöfian, nowhere locally complete, fixed point
Article copyright: © Copyright 1970 American Mathematical Society