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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Open mappings of the universal curve onto continuous curves


Author: David C. Wilson
Journal: Trans. Amer. Math. Soc. 168 (1972), 497-515
MSC: Primary 54F50
MathSciNet review: 0298630
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Abstract: A criterion for the existence of an open mapping from one compact metric space onto another is established in this paper. This criterion is then used to establish the existence of a monotone open mapping of the universal curve onto any continuous curve and the existence of a light open mapping of the universal curve onto any nondegenerate continuous curve. These examples show that if $ f$ is a monotone open or a light open mapping of one compact space $ X$ onto another $ Y$, then it will not necessarily be the case that $ \dim Y \leqq \dim X + k$, where $ k$ is some positive integer.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0298630-0
PII: S 0002-9947(1972)0298630-0
Article copyright: © Copyright 1972 American Mathematical Society