We are inspired by the work of Henri Cartan [16], Bourbaki [10] (TG. I Filtres) and Claude Wagschal [34]. We define the base of filter, image filter, convergent filter bases, limit filter and the filter base of tails (fr: filtre des sections).
In this paper, two kinds of remote neighborhood operators in -fuzzy convex spaces are proposed, which are called convex -fuzzy remote neighborhood operators. It is proved that these two kinds of convex -fuzzy remote neighborhood operators can be used to characterize -fuzzy convex structures. In addition, the lattice structures of two kinds of convex -fuzzy remote neighborhood operators are also given.
We show that, under CH, the corona of a countable ultrametric space is homeomorphic to . As a corollary, we get the same statements for the Higson’s corona of a proper ultrametric space and the space of ends of a countable locally finite group.