Every exactly -to- function on the reals has an infinite set of discontinuities

Author:
Jo Heath

Journal:
Proc. Amer. Math. Soc. **98** (1986), 369-373

MSC:
Primary 54C10; Secondary 26A15

DOI:
https://doi.org/10.1090/S0002-9939-1986-0854049-8

MathSciNet review:
854049

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It has long been known that the set of discontinuities of a -to- function on either the closed or the open interval must be nonempty; this paper proves that the set must be infinite.

**[1]**K. Borsuk and R. Molski,*On a class of continuous maps*, Fund. Math.**45**(1958), 84-98. MR**0102063 (21:858)****[2]**P. Civin,*Two-to-one mappings of manifolds*, Duke Math. J.**10**(1943), 49-57. MR**0008697 (5:47e)****[3]**P. Gilbert,*-to-one mappings of linear graphs*, Duke Math. J.**9**(1942), 475-486. MR**0007106 (4:88b)****[4]**O. G. Harrold,*The non-existence of a certain type of continuous transformation*, Duke Math. J.**5**(1939), 789-793. MR**0001358 (1:223c)****[5]**-,*Exactly*)*transformations on connected linear graph*, Amer. J. Math.**62**(1940), 823-834. MR**0002554 (2:75c)****[6]**V. Martin and J. H. Roberts,*Two-to-one transformations on**-manifolds*, Trans. Amer. Math. Soc.**49**(1941), 1-17. MR**0004129 (2:324d)****[7]**J. Mioduszewski,*On two-to-one continuous functions*, Dissertationes Math. (Rozprawy Mat.)**24**(1961), 42. MR**0145490 (26:3021)****[8]**S. B. Nadler, Jr., and L. W. Ward, Jr.,*Concerning exactly*)*images of continua*, Proc. Amer. Math. Soc.**87**(1983), 351-354. MR**681847 (84c:54059)****[9]**J. H. Roberts,*Two-to-one transformation*,. Duke Math. J.**6**(1940), 256-262. MR**0001923 (1:319d)**

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

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

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0854049-8

Article copyright:
© Copyright 1986
American Mathematical Society