Vol. 8, No. 1, 2015

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Nonultrametric triangles in diametral additive metric spaces

Timothy Faver, Katelynn Kochalski, Mathav Kishore Murugan, Heidi Verheggen, Elizabeth Wesson and Anthony Weston

Vol. 8 (2015), No. 1, 33–37
Abstract

We prove that a diametral additive metric space is not ultrametric if and only if it contains a diameter attaining nonultrametric triangle.

Keywords
ultrametric spaces, additive metric spaces, tree metrics
Mathematical Subject Classification 2010
Primary: 54E35
Secondary: 51F99
Milestones
Received: 20 June 2012
Accepted: 10 January 2013
Published: 10 December 2014

Communicated by Toka Diagana
Authors
Timothy Faver
Department of Mathematics
Drexel University
Philadelphia, PA 19104
United States
Katelynn Kochalski
Department of Mathematics
University of Virginia
Charlottesville, VA 22904
United States
Mathav Kishore Murugan
Center for Applied Mathematics
Cornell University
Ithaca, NY 14853
United States
Heidi Verheggen
Department of Economics
University of Pennsylvania
Philadelphia, PA 19104
United State
Elizabeth Wesson
Center for Applied Mathematics
Cornell University
Ithaca, NY 14853
United States
Anthony Weston
Faculty of Arts and Sciences
Australian Catholic University
North Sydney, NSW 2060
Australia
Department of Mathematics and Statistics
Canisius College
Buffalo, NY 14208
United States