Quasi-completion of filter spaces

© 2015 Academic Publications, Ltd. The category FIL 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 FIL. 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 FIL comprising all filter spaces as objects.