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Licensed Unlicensed Requires Authentication Published by De Gruyter September 22, 2017

Unified approach to graphs and metric spaces

  • Jan Pavlík EMAIL logo
From the journal Mathematica Slovaca


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.

MSC 2010: 54E35; 06F05

The support was provided by Brno University of Technology, specific research plan no. FSI-S-17-4464.

(Communicated by Jiří Rachůnek)


The author gratefully acknowledges useful comments and advice of Sergej Solovjov, Jan Paseka and Jiří Rachůnek.


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Received: 2015-2-2
Accepted: 2017-1-26
Published Online: 2017-9-22
Published in Print: 2017-10-26

© 2017 Mathematical Institute Slovak Academy of Sciences

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