Metric spaces, generalized logic, and closed categories

  • F. William Lawvere


The analogy between dist (a, b)+dist (b, c)≥dist (a, c) and hom (A, B) ⊗ hom (B, C)→hom (A, C) is rigorously developed to display many general results about metric spaces as consequences of a «generalized pure logic» whose «truth-values» are taken in an arbitrary closed category.


Natural Transformation Isometric Embedding Generalize Logic Ultrametric Space Forgetful Functor 
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In questo articolo viene rigorosamente sviluppata l'analogia fra dist (a, b)+dist (b, c)≥dist (a, c) e hom (A, B) ⊗ hom (B, C)→ hom (A, C), giungendo a numerosi risultati generali sugli spazi metrici, come conseguenza di una «logica pura generalizzata» i cui «valori di verità» sono scelti in una arbitraria categoria chiusa.


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  3. Benabou Jean,Les Distributeurs, Raport no 33, janvier 1973, Seminaires de Mathématiques Pure, Institut de Mathématiques, Université Catholique de Louvain (multigraphed).Google Scholar

Copyright information

© Birkhäuser-Verlag 1973

Authors and Affiliations

  • F. William Lawvere
    • 1
  1.' Università di PerugiaPerugiaItalia

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