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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Concerning continuous images of rim-metrizable continua


Author: H. Murat Tuncali
Journal: Proc. Amer. Math. Soc. 113 (1991), 461-470
MSC: Primary 54C10; Secondary 54F05, 54F15
MathSciNet review: 1069694
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Abstract: Mardesic (1962) proved that if $ X$ is a continuous, Hausdorff, infinite image of a compact ordered space $ K$ under a light mapping in the sense of ordering, then $ \omega (X) = \omega (K)$. He also proved (1967) that a continuous, Hausdorff image of a compact ordered space is rim-metrizable. Treybig (1964) proved that the product of two infinite nonmetrizable compact Hausdorff spaces cannot be a continuous image of a compact ordered space.

We prove some analogues of these results for continuous Hausdorff images of rim-metrizable spaces.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1069694-9
PII: S 0002-9939(1991)1069694-9
Article copyright: © Copyright 1991 American Mathematical Society