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Approach Spaces, Limit Tower Spaces, and Probabilistic Convergence Spaces

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Abstract

The category LTS of limit tower spaces is defined and shown to be isomorphic to the category CAP of convergence approach spaces. The full subcategory of LTS determined by the objects satisfying a diagonal axiom due to Cook and Fischer is shown to be isomorphic to the category AP of approach spaces. A family of isomorphisms is also obtained between LTS and certain full subcategories of the category PCS of probabilistic convergence spaces.

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, Washington State University, Pullman, WA, 99164-3113, U.S.A.

    Paul Brock & D. C. Kent

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  1. Paul Brock
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  2. D. C. Kent
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Brock, P., Kent, D.C. Approach Spaces, Limit Tower Spaces, and Probabilistic Convergence Spaces. Applied Categorical Structures 5, 99–110 (1997). https://doi.org/10.1023/A:1008633124960

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  • DOI: https://doi.org/10.1023/A:1008633124960

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