-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
Full-text PDF
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