Closure spaces and characterizations of filters in terms of their Stone images

Anh Tran Mynard; Frédéric Mynard

Czechoslovak Mathematical Journal (2007)

  • Volume: 57, Issue: 3, page 1025-1034
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Mynard, Anh Tran, and Mynard, Frédéric. "Closure spaces and characterizations of filters in terms of their Stone images." Czechoslovak Mathematical Journal 57.3 (2007): 1025-1034. <http://eudml.org/doc/31179>.

@article{Mynard2007,
abstract = {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.},
author = {Mynard, Anh Tran, Mynard, Frédéric},
journal = {Czechoslovak Mathematical Journal},
keywords = {filters; ultrafilters; Frechet; closure spaces; filters; ultrafilters; Frechet; closure spaces},
language = {eng},
number = {3},
pages = {1025-1034},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Closure spaces and characterizations of filters in terms of their Stone images},
url = {http://eudml.org/doc/31179},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Mynard, Anh Tran
AU - Mynard, Frédéric
TI - Closure spaces and characterizations of filters in terms of their Stone images
JO - Czechoslovak Mathematical Journal
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 3
SP - 1025
EP - 1034
AB - 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.
LA - eng
KW - filters; ultrafilters; Frechet; closure spaces; filters; ultrafilters; Frechet; closure spaces
UR - http://eudml.org/doc/31179
ER -

References

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