There is no exactly -to- function from any continuum onto , or any dendrite, with only finitely many discontinuities

Author:
Jo W. Heath

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

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Abstract: Katsuura and Kellum recently proved [**8**] that any (exactly) -to function from onto 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) -to- function from a continuum onto any dendrite has finitely many discontinuities, answers their question in the affirmative.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1988-0927692-1

Keywords:
-to- function,
-to- map

Article copyright:
© Copyright 1988
American Mathematical Society