The structure of (exactly) -to- maps on metric compacta

Author:
Jo Heath

Journal:
Proc. Amer. Math. Soc. **110** (1990), 549-555

MSC:
Primary 54C10

DOI:
https://doi.org/10.1090/S0002-9939-1990-1013970-1

MathSciNet review:
1013970

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that the domain of a -to- continuous map contains two disjoint open sets and such that and is a homeomorphism from onto a dense open subset of the image of . The restriction of to is the first "fold", and is shown to be the union of a finite or transfinite sequence of similar folds.

**[1]**O. G. Harrold,*The non-existence of a certain type of continuous transformation*, Duke Math. J.**5**(1939), 789-793. MR**0001358 (1:223c)****[2]**Jo 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)****[3]**-,*-to-**functions on arcs for**even*, Proc. Amer. Math. Soc.**101**(1987), 387-391. MR**902560 (89b:26002)****[4]**-,*-to-**functions between graphs with finitely many discontinuities*, Proc. Amer. Math. Soc.**103**(1988), 661-666. MR**943101 (89i:05104)****[5]**-,*Tree-like continua and exactly**-to-**functions*, Proc. Amer. Math. Soc.**105**(1989),**[6]**J. Mioduszewski,*On two-to-one continuous functions*, Dissertationes Math. (Rozprawy Mat.)**24**(1961), 42. MR**0145490 (26:3021)****[7]**J. H. Roberts,*Two-to-one transformations*, Duke Math. J.**6**(1940), 256-262. MR**0001923 (1:319d)**

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

Retrieve articles in all journals with MSC: 54C10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1013970-1

Keywords:
-to- function,
-to- map,
-to- map,
-to- function

Article copyright:
© Copyright 1990
American Mathematical Society