-to-
functions on arcs for
even
Author:
Jo W. Heath
Journal:
Proc. Amer. Math. Soc. 101 (1987), 387-391
MSC:
Primary 26A15; Secondary 54C10
DOI:
https://doi.org/10.1090/S0002-9939-1987-0902560-4
MathSciNet review:
902560
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Abstract | References | Similar Articles | Additional Information
Abstract: For exactly -to-
functions from
into
:
(1) at least one discontinuity is required (Harrold),
(2) if , then infinitely many discontinuities are needed, for any Hausdorff image space (Heath),
(3) if , or if
is odd, then there is such a function with only one discontinuity (Katsuura and Kellum), and, it is shown here that
(4) if is even and
, then there is such a function with only two discontinuities, and no such function exists with fewer discontinuities.
- [1]
P. Gilbert,
-to-one mappings of linear graphs, Duke Math. J. 9 (1942), 475-486. MR 0007106 (4:88b)
- [2]
O. G. Harrold, Jr., Exactly
transformations on connected linear graphs, Amer. J. Math. 62 (1940), 823-834. MR 0002554 (2:75c)
- [3]
J. W. Heath, Every exactly
-to-
function on the reals has an infinite number of discontinuities, Proc. Amer. Math. Soc. 98 (1986), 369-373. MR 854049 (87i:54031)
- [4]
H. Katsuura and K. Kellum,
-to-
functions on an arc, preprint.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1987-0902560-4
Keywords:
-to-
function,
-to-
map
Article copyright:
© Copyright 1987
American Mathematical Society