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The Structure of (Exactly) 2-To-1 Maps on Metric Compacta
Proceedings of the American Mathematical Society
Vol. 110, No. 2 (Oct., 1990), pp. 549-555
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2048103
Page Count: 7
You can always find the topics here!Topics: Mathematical functions, Homeomorphism, Mathematical sequences, Function discontinuity, Diameters, Coordinate systems, Integers, Glues
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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.
Proceedings of the American Mathematical Society © 1990 American Mathematical Society