Unified approach to graphs and metric spaces

Jan Pavlík 1
  • 1 Faculty of Mechanical Engineering Brno University of Technology, Brno, Czech Republic
Jan Pavlík
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  • Faculty of Mechanical Engineering Brno University of Technology, Brno, Czech Republic
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Abstract

The paper provides a generalization of a metric with values in a general structure. Quantales and special kinds of ordered monoids are shown to be suitable for this purpose. Topological and categorical properties of spaces with such generalized metrics are studied and a special emphasis is given on paths in these spaces.

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