A parametrization theorem |
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Authors: | G Mägerl RDaniel Mauldin E Michael |
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Institution: | Universität Erlangen-Nürnberg, Fed. Rep. Germany;North Texas State University, Denton, TX, U.S.A.;University of Washington, Seattle, WA, U.S.A. |
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Abstract: | The following result, and a closely related one, is proved: If u:X → Y is an open, perfect surjection, with X metrizable and with dim X = 0 or dim Y = 0, then there exists a perfect surjection such that u ° h = πY (where S in the Cantor set and is the projection). If moreover, u-1(y) is homeomorphic to S for all y?Y, then h can be chosen to be a homeomorphism. |
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Keywords: | 54C10 54C25 54C65 54F45 54F99 Cantor set perfect maps open maps homeomorphisms continuous selections zero-dimensional spaces |
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