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The Structure of (Exactly) 2-To-1 Maps on Metric Compacta

Jo Heath
Proceedings of the American Mathematical Society
Vol. 110, No. 2 (Oct., 1990), pp. 549-555
DOI: 10.2307/2048103
Stable URL: http://www.jstor.org/stable/2048103
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Structure of (Exactly) 2-To-1 Maps on Metric Compacta
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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 $\widehat V$ such that $f(V) = f(\widehat V)$ and $f \upharpoonright V$ is a homeomorphism from V onto a dense open subset of the image of f. The restriction of f to $V \cup \widehat V$ 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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