Abstract
Not every nearness space can be extended to a topological space. The nearness spaces that can be so extended turn out to have a neat internal characterization: The condition is that every nearness collection should be a subset of some bunch. For those nearness spaces, the extension process gives rise to a functor, that is, nearness preserving maps are all extendible. To have a more convenient language in which to express the results, certain categories are defined and certain functors are studied. The first such category is a category denoted Ex whose objects are certain continuous maps. The chapter discusses grills and bunches to define a functor G:Near→Ex. The chapter discusses a certain full subcategory Bun of Near. Bun is a bicoreflective subcategory of Near and the restrictions to Bun of the functors have many nice properties.
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