On Expansive Mappings

Marat V. Markin and Edward S. Sichel
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Marat V. Markin: Department of Mathematics, California State University, Fresno 5245 N. Backer Avenue, M/S PB 108, Fresno, CA 93740-8001, USA
Edward S. Sichel: Department of Mathematics, California State University, Fresno 5245 N. Backer Avenue, M/S PB 108, Fresno, CA 93740-8001, USA

Mathematics, 2019, vol. 7, issue 11, 1-10

Abstract: 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 .

Keywords: metric space; expansion; compactness; total boundedness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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