Geodesic
Closure spaces and characterizations of filters in terms of their Stone images
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 1025-1034 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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 
@article{CMJ_2007_57_3_a17,
     author = {Mynard, Anh Tran and Mynard, Fr\'ed\'eric},
     title = {Closure spaces and characterizations of filters in terms of their {Stone} images},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1025--1034},
     year = {2007},
     volume = {57},
     number = {3},
     mrnumber = {2356937},
     zbl = {1174.54001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a17/}
}
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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/