Convergent Filter Bases

نویسنده

Roland Coghetto

چکیده

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). The notation and terminology used in this paper have been introduced in the From now on X denotes a non empty set, F denotes a filter of X, and S denotes a family of subsets of X. Let X be a set and S be a family of subsets of X. We say that S is upper if and only if (Def. 1) for every subsets Y 1 , Y 2 of X such that Y 1 ∈ S and Y 1 ⊆ Y 2 holds Y 2 ∈ S. Let us note that there exists a ∩-closed family of subsets of X which is non empty and there exists a non empty, ∩-closed family of subsets of X which is upper. Let X be a non empty set. Let us note that there exists a non empty, upper, ∩-closed family of subsets of X which has non empty elements. Now we state the propositions:

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