An Access Theorem for Continuous Functions |
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Authors: | Borichev, Alexander Kleschevich, Igor |
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Affiliation: | Department of Mathematics, University of Bordeaux I 351 cours de la Liberation, 33405 Talence, France, borichev{at}math.u-bordeaux.fr 19 Mount Hood Road 4, Brighton, MA 02215, USA |
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Abstract: | Let f be a continuous function on an open subset of R2 suchthat for every x there exists a continuous map : [1,1] with (0) = x and f increasing on [1, 1]. Thenfor every there exists a continuous map : [0, 1) suchthat (0) = y, f is increasing on [0; 1), and for every compactsubset K of , max{t : (t) K} < 1. This result gives an answerto a question posed by M. Ortel. Furthermore, an example showsthat this result is not valid in higher dimensions. |
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