IJPAM: Volume 104, No. 3 (2015)
School of Mathematics and Statistics
University of Western Australia
Crawley, W.A. 6009, AUSTRALIA
Abstract. The category of filter spaces being isomorphic to the category of grill-determined nearness spaces has become significant in the later part of the twentieth century. During that period, a substantial completion theory has been developed using the equivalence classes of filters in a filter space. However, that completion was quite general in nature, and did not allow the finest such completion. As a result, a completion functor could not be defined on . In this paper, this issue is partially addressed by constructing a completion that is finer than the existing completions. Also, a completion functor is defined on a subcategory of comprising all filter spaces as objects.
Received: August 16, 2015
AMS Subject Classification: 54D35, 54A20, 54C20
Key Words and Phrases: filter space, Cauchy map, convergence structure, -map, stable completion, completion in standard form
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DOI: 10.12732/ijpam.v104i3.13 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 461 - 470