Open mappings of the universal curve onto continuous curves
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- by David C. Wilson PDF
- Trans. Amer. Math. Soc. 168 (1972), 497-515 Request permission
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.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 168 (1972), 497-515
- MSC: Primary 54F50
- DOI: https://doi.org/10.1090/S0002-9947-1972-0298630-0
- MathSciNet review: 0298630