-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