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Proceedings of the American Mathematical Society

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

 
 

 

The structure of (exactly) $ 2$-to-$ 1$ 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
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Abstract: It is shown that the domain of a $ 2$-to-$ 1$ continuous map $ f$ contains two disjoint open sets $ V$ and $ {V^ \wedge }$ such that $ f\left( V \right) = f\left( {{V^ \wedge }} \right)$ and $ f \upharpoonright V$ is a homeomorphism from $ V$ onto a dense open subset of the image of $ f$. The restriction of $ f$ to $ V \cup {V^ \wedge }$ is the first "fold", and $ f$ is shown to be the union of a finite or transfinite sequence of similar folds.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1013970-1
Keywords: $ k$-to-$ 1$ function, $ 2$-to-$ 1$ map, $ k$-to-$ 1$ map, $ 2$-to-$ 1$ function
Article copyright: © Copyright 1990 American Mathematical Society

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