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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  10. On weakly bisequential spaces, Comment. Math. Univ. Carolinae 41 (2000), 611–617. (2000) MR1795090
  11. On countable spaces having no bicompactification of countable tightness, Dokl. Akad. Nauk SSSR 206 (1972), 1407–1411. (1972) Zbl0263.54015MR0320981
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