Metric 1-spaces

Publication date: 19 January 2012

Abstract: A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and equivalent, axiomatization of metric space is given which is then generalized from a fresh point of view. Naturally arising examples from metric geometry are presented.

Mathematics Subject Classification ID

Metric geometry (51F99)

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