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Subcategories of Filter Tower Spaces

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Abstract

The concept of a convergence tower space, or equivalently, a convergence approach space is formulated here in the context of a Cauchy setting in order to include a completion theory. Subcategories of filter tower spaces are defined in terms of axioms involving a general t-norm, T, in order to include a broad range of spaces. A T-regular sequence for a filter tower space is defined and, moreover, it is shown that the category of T-regular objects is a bireflective subcategory of all filter tower spaces. A completion theory for subcategories of filter tower spaces is given.

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References

  1. Adámek, J., Herrlich, H. and Strecker, G.: Abstract and Concrete Categories, J. Wiley, 1990.

  2. Brock, P. and Kent, D.: Approach spaces, limit tower spaces and probabilistic convergence spaces, Appl. Categorical Structures 5 (1997), 99-110.

    Google Scholar 

  3. Floresque, L.: A p-complete Menger structure for distribution functions space, An. Stiint Univ. 'Al. I. Cuza' Iasi 34 (1988), 1-6.

    Google Scholar 

  4. Floresque, L.: Probabilistic convergence structures, Aeq. Math. 38 (1989), 123-145.

    Google Scholar 

  5. Herrlich, H. and Zhang, D.: Categorical properties of probabilistic convergence spaces (manuscript).

  6. Kent, D. and Richardson, G.: Completions of probabilistic Cauchy spaces, Math. Japon. (to appear).

  7. Lowen, E. and Lowen, R.: A quasi topos containing CONV and MET as full subcategories, Intl. J. Math. and Math. Sci. 11 (1988), 417-438.

    Google Scholar 

  8. Lowen, E. and Lowen, R.: Topological quasitopos hulls of categories containing topological and metric objects, Cahiers de Top. et Geom. Diff. Cat. 30 (1989), 213-228.

    Google Scholar 

  9. Lowen, R.: Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad, Oxford University Press Inc., 1997.

  10. Menger, K.: Statistical metrics, Proc. Nat. Acad. Sci. USA 28 (1942), 535-537.

    Google Scholar 

  11. Minkler, J., Minkler, G. and Richardson, G.: T-regular probabilistic convergence spaces, J. Austral. Math. Soc. (Series A) (to appear).

  12. Preuss, G.: Theory of Topological Structures: An Approach to Categorical Topology, D. Reidel Pub. Co., 1988.

  13. Preuss, G.: Improvement of Cauchy spaces, Q & A in General Topology 9 (1991), 159-166.

    Google Scholar 

  14. Preuss, G.: Cauchy spaces and generalizations, Math. Japon. 38 (1993), 803-812.

    Google Scholar 

  15. Preuss, G.: Semiuniform limit spaces and semi-Cauchy spaces (manuscript).

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Authors and Affiliations

  1. University of Central Florida, Department of Mathematics, Orlando, FL, 32816-1364, USA

    J. Minkler, G. Minkler & G. Richardson

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  1. J. Minkler
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  2. G. Minkler
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  3. G. Richardson
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Minkler, J., Minkler, G. & Richardson, G. Subcategories of Filter Tower Spaces. Applied Categorical Structures 9, 369–379 (2001). https://doi.org/10.1023/A:1011226611840

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