SIMULTANEOUS EXTENSIONS OF TOPOLOGIES THROUGH TRACES OF NEIGHBOURHOOD FILTERS


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Abstract

Let X be a set, XiX for iI and, for xX, (x) filter in Xi. The paper gives necessary and sufficient conditions for the existence of a topology τ on X compatible with, i.e. such that is the trace on Xi of the τ-neighbourhood filter of x. It is shown that, among these compatible topologies,there are always a coarsest one and a finest one. Some applications are also given.

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