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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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