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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the existence of exactly $ (2,1)$ maps


Author: R. E. Smithson
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
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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$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0875403-5
Keywords: Exactly $ n$-to-1 maps, continua, cutpoints, nested continua
Article copyright: © Copyright 1987 American Mathematical Society