We define a binary metric as a symmetric, distributive lattice ordered magma-valued function of two variables, satisfying a “triangle inequality". Using the notion of a Kuratowski topology, in which topologies are specified by closed sets rather than open sets, we prove that every topology is induced by a binary metric. We conclude with a discussion on the relation between binary metrics and some separation axioms.
S. Assaf et al., "Binary Metrics," Topology and its Applications, vol. 274, Elsevier, Apr 2020.
The definitive version is available at https://doi.org/10.1016/j.topol.2020.107116
Mathematics and Statistics
Keywords and Phrases
Binary metric; Generalized metric; Partial metric
International Standard Serial Number (ISSN)
Article - Journal
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01 Apr 2020