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Proceedings of the American Mathematical Society

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

 
 

 

Ordered spaces all of whose continuous images are normal


Authors: William Fleissner and Ronnie Levy
Journal: Proc. Amer. Math. Soc. 105 (1989), 231-235
MSC: Primary 54F05; Secondary 54D15
DOI: https://doi.org/10.1090/S0002-9939-1989-0973846-4
MathSciNet review: 973846
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Abstract: Some spaces, such as compact Hausdorff spaces, have the property that every regular continuous image is normal. In this paper, we look at such spaces. In particular, it is shown that if a normal space has finite Stone-Čech remainder, then every continuous image is normal. A consequence is that every continuous image of a Dedekind complete linearly ordered topological space of uncountable cofinality and coinitiality is normal. The normality of continuous images of other ordered spaces is also discussed.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0973846-4
Article copyright: © Copyright 1989 American Mathematical Society

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