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On Expansive Mappings

Department of Mathematics, California State University, Fresno 5245 N. Backer Avenue, M/S PB 108, Fresno, CA 93740-8001, USA
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Mathematics 2019, 7(11), 1004; https://doi.org/10.3390/math7111004
Received: 23 August 2019 / Revised: 23 September 2019 / Accepted: 17 October 2019 / Published: 23 October 2019
(This article belongs to the Special Issue Noncommutative Geometry and Number Theory)
When finding an original proof to a known result describing expansive mappings on compact metric spaces as surjective isometries, we reveal that relaxing the condition of compactness to total boundedness preserves the isometry property and nearly that of surjectivity. While a counterexample is found showing that the converse to the above descriptions do not hold, we are able to characterize boundedness in terms of specific expansions we call anticontractions. View Full-Text
Keywords: metric space; expansion; compactness; total boundedness metric space; expansion; compactness; total boundedness
MDPI and ACS Style

Markin, M.V.; Sichel, E.S. On Expansive Mappings. Mathematics 2019, 7, 1004.

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