-to- functions on an arc

Authors:
Hidefumi Katsuura and Kenneth R. Kellum

Journal:
Proc. Amer. Math. Soc. **101** (1987), 629-633

MSC:
Primary 54C10; Secondary 54C30, 54F15

DOI:
https://doi.org/10.1090/S0002-9939-1987-0911022-X

MathSciNet review:
911022

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Abstract | References | Similar Articles | Additional Information

Abstract: Recently Jo W. Heath [**6**] has shown that any -to- function from an arc onto a Hausdorff space must have infinitely many discontinuities. Here we investigate extending Heath's result to -to- functions for . Examples show that in general Heath's theorem cannot be extended even for functions from an arc into itself. However, if is a -to- function from an arc *onto* an arc, then we prove that has infinitely many discontinuities.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1987-0911022-X

Keywords:
-to- function,
-to- function

Article copyright:
© Copyright 1987
American Mathematical Society