On the existence of exactly $(2,1)$ maps
HTML articles powered by AMS MathViewer
- by R. E. Smithson PDF
- Proc. Amer. Math. Soc. 99 (1987), 577-580 Request permission
Abstract:
The following two theorems concerning the existence of exactly 2 to 1 maps are proved. If $Y$ is a continuum such that each nondegenerate subcontinuum contains a cutpoint, then there does not exist a continuum $X$ and an exactly 2 to 1 map on $X$ onto $Y$. Further, if $X$ is an arcwise connected continuum and $Y$ is a nested continuum, then there does not exist an exactly 2 to 1 map on $X$ onto $Y$.References
- Charles O. Christenson and William L. Voxman, Aspects of topology, Pure and Applied Mathematics, Vol. 39, Marcel Dekker, Inc., New York-Basel, 1977. MR 0487938
- Paul Civin, Two-to-one mappings of manifolds, Duke Math. J. 10 (1943), 49–57. MR 8697 J. K. Harris, Order structures for certain acyclic topological spaces, Thesis, Univ. of Oregon, 1962.
- O. G. Harrold Jr., The non-existence of a certain type of continuous transformation, Duke Math. J. 5 (1939), 789–793. MR 1358
- O. G. Harrold Jr., Exactly $(k,1)$ transformations on connected linear graphs, Amer. J. Math. 62 (1940), 823–834. MR 2554, DOI 10.2307/2371492
- Sam B. Nadler Jr. and L. E. Ward Jr., Concerning exactly $(n,\,1)$ images of continua, Proc. Amer. Math. Soc. 87 (1983), no. 2, 351–354. MR 681847, DOI 10.1090/S0002-9939-1983-0681847-3
- J. H. Roberts, Two-to-one transformations, Duke Math. J. 6 (1940), 256–262. MR 1923, DOI 10.1215/S0012-7094-40-00620-2
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 577-580
- MSC: Primary 54F15; Secondary 54C10, 54F20, 54F50
- DOI: https://doi.org/10.1090/S0002-9939-1987-0875403-5
- MathSciNet review: 875403