Abstract
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.
Recommended Citation
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
Department(s)
Mathematics and Statistics
Keywords and Phrases
Binary metric; Generalized metric; Partial metric
International Standard Serial Number (ISSN)
0166-8641; 1879-3207
Document Type
Article - Journal
Document Version
Preprint
File Type
text
Language(s)
English
Rights
© 2020 Elsevier, All rights reserved.
Publication Date
01 Apr 2020
