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Proceedings of the American Mathematical Society

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

 

 

A short proof that a compact ordered space cannot be mapped onto a nonmetric product


Authors: W. Bula, W. Dębski and W. Kulpa
Journal: Proc. Amer. Math. Soc. 82 (1981), 312-313
MSC: Primary 54F05; Secondary 54E35
MathSciNet review: 609675
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Abstract: In this note we give an elementary proof of a theorem of Treybig: if a product $ X \times Y $ of two infinite Hausdorff spaces is a continuous image of a compact linearly ordered space, then $ X \times Y$ is metrizable.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0609675-3
Article copyright: © Copyright 1981 American Mathematical Society