-to- functions on arcs for even

Author:
Jo W. Heath

Journal:
Proc. Amer. Math. Soc. **101** (1987), 387-391

MSC:
Primary 26A15; Secondary 54C10

MathSciNet review:
902560

Full-text PDF Free Access

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]**Paul W. Gilbert,*𝑛-to-one mappings of linear graphs*, Duke Math. J.**9**(1942), 475–486. MR**0007106****[2]**O. G. Harrold Jr.,*Exactly (𝑘,1) transformations on connected linear graphs*, Amer. J. Math.**62**(1940), 823–834. MR**0002554****[3]**Jo Heath,*Every exactly 2-to-1 function on the reals has an infinite set of discontinuities*, Proc. Amer. Math. Soc.**98**(1986), no. 2, 369–373. MR**854049**, 10.1090/S0002-9939-1986-0854049-8**[4]**H. Katsuura and K. Kellum,*-to-**functions on an arc*, preprint.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
26A15,
54C10

Retrieve articles in all journals with MSC: 26A15, 54C10

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