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), 293305
MSC:
Primary 54C10; Secondary 54F15, 54F50
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:
http://dx.doi.org/10.1090/S00029947198809276921
PII:
S 00029947(1988)09276921
Keywords:
to function,
to map
Article copyright:
© Copyright 1988
American Mathematical Society
