# 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

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topMynard, 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

top- Bisequential spaces, tightness of products, and metrizability conditions in topological groups, Trans. Moscow Math. Soc. 55 (1994), 207–219. (1994) MR1468459
- Single non-isolated point space, Rend. Istit. Mat. Univ. Trieste 28 (1996), 101–113. (1996) MR1463912
- 10.1016/0166-8641(96)00067-3, Topology Appl. 73 (1996), 1–21. (1996) MR1413721DOI10.1016/0166-8641(96)00067-3
- Private communication (2003), .
- The ABC of order and topology, Category Theory at Work (H. Herrlich and H.-E. Porst, eds.), Heldermann, 1991, pp. 57–83. (1991) MR1147919
- Finite products of filters that are compact relative to a class of filters, Applied General Topology (to appear). (to appear) MR2398508
- 10.1016/S1631-073X(02)02473-1, C. R. Acad. Sci. Paris, Ser I 335 (2002), 259–262. (2002) MR1933669DOI10.1016/S1631-073X(02)02473-1
- 10.1007/s10587-004-6446-0, Czech. Math. J. 54 (2004), 981–990. (2004) MR2100010DOI10.1007/s10587-004-6446-0
- 10.1016/j.topol.2005.08.008, Topopogy Appl. 153 (2006), 2386–2412. (2006) MR2243719DOI10.1016/j.topol.2005.08.008
- On weakly bisequential spaces, Comment. Math. Univ. Carolinae 41 (2000), 611–617. (2000) MR1795090
- On countable spaces having no bicompactification of countable tightness, Dokl. Akad. Nauk SSSR 206 (1972), 1407–1411. (1972) Zbl0263.54015MR0320981
- 10.1016/0016-660X(72)90040-2, Gen. Topology Appl. 2 (1972), 91–138. (1972) Zbl0238.54009MR0309045DOI10.1016/0016-660X(72)90040-2
- 10.1016/0016-660X(74)90002-6, Topology Appl. 4 (1974), 1–28. (1974) MR0365463DOI10.1016/0016-660X(74)90002-6

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