Geodesic
Closure spaces and characterizations of filters in terms of their Stone images
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 1025-1034.

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Fréchet, strongly Fréchet, productively Fréchet, weakly bisequential and bisequential filters (i.e., neighborhood filters in spaces of the same name) are characterized in a unified manner in terms of their images in the Stone space of ultrafilters. These characterizations involve closure structures on the set of ultrafilters. The case of productively Fréchet filters answers a question of S. Dolecki and turns out to be the only one involving a non topological closure structure.
Classification : 54A05, 54A20, 54D55
Keywords: filters; ultrafilters; Frechet; closure spaces 
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     title = {Closure spaces and characterizations of filters in terms of their {Stone} images},
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Mynard, Anh Tran; Mynard, Frédéric. Closure spaces and characterizations of filters in terms of their Stone images. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 1025-1034. http://geodesic.mathdoc.fr/item/CMJ_2007__57_3_a17/