Approach Spaces, Limit Tower Spaces, and Probabilistic Convergence Spaces |
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Authors: | Paul Brock D C Kent |
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Institution: | (1) Department of Pure and Applied Mathematics, Washington State University, Pullman, WA, 99164-3113, U.S.A. |
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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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Keywords: | approach space convergence approach limit limit tower isomorphism functor probabilistic convergence space t-norm |
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