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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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There is no exactly $k$-to-$1$ function from any continuum onto $[0,1]$, or any dendrite, with only finitely many discontinuities
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by Jo W. Heath PDF
Trans. Amer. Math. Soc. 306 (1988), 293-305 Request permission

Abstract:

Katsuura and Kellum recently proved [8] that any (exactly) $k$-to$1$ function from $[0, 1]$ onto $[0, 1]$ must have infinitely many discontinuities, and they asked if the theorem remains true if the domain is any (compact metric) continuum. The result in this paper, that any (exactly) $k$-to-$1$ function from a continuum onto any dendrite has finitely many discontinuities, answers their question in the affirmative.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 306 (1988), 293-305
  • MSC: Primary 54C10; Secondary 54F15, 54F50
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0927692-1
  • MathSciNet review: 927692