Binary metrics. (English) Zbl 1435.54001
Summary: 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.
MSC:
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 54D10 | Lower separation axioms (\(T_0\)–\(T_3\), etc.) |
| 54E35 | Metric spaces, metrizability |
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