Subcategories of Filter Tower Spaces |
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Authors: | J Minkler G Minkler G Richardson |
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Institution: | 1. University of Central Florida, Department of Mathematics, Orlando, FL, 32816-1364, USA
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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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Keywords: | filter tower spaces convergence approach spaces completions t-norm T-regular sequences |
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