Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
filters; ultrafilters; Frechet; closure spaces
filters; ultrafilters; Frechet; closure spaces
Summary:
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.
References:
[1] A. V. Arhangel’skii: Bisequential spaces, tightness of products, and metrizability conditions in topological groups. Trans. Moscow Math. Soc. 55 (1994), 207–219. MR 1468459
[2] A. Bella and V. I. Malykhin: Single non-isolated point space. Rend. Istit. Mat. Univ. Trieste 28 (1996), 101–113. MR 1463912
[3] S. Dolecki: Convergence-theoretic methods in quotient quest. Topology Appl. 73 (1996), 1–21. DOI 10.1016/0166-8641(96)00067-3 | MR 1413721
[4] S. Dolecki: Private communication (2003).
[5] Marcel Erné: The ABC of order and topology. Category Theory at Work (H. Herrlich and H.-E. Porst, eds.), Heldermann, 1991, pp. 57–83. MR 1147919
[6] I. Labuda, F. Jordan and F. Mynard: Finite products of filters that are compact relative to a class of filters. Applied General Topology (to appear). MR 2398508
[7] F. Jordan and F. Mynard: Espaces productivement de Fréchet. C. R. Acad. Sci. Paris, Ser I 335 (2002), 259–262. DOI 10.1016/S1631-073X(02)02473-1 | MR 1933669
[8] F. Jordan and F. Mynard: Productively Fréchet spaces. Czech. Math. J. 54 (2004), 981–990. DOI 10.1007/s10587-004-6446-0 | MR 2100010
[9] F. Jordan and F. Mynard: Compatible relations on filters and stability of local topological properties under supremum and product. Topopogy Appl. 153 (2006), 2386–2412. DOI 10.1016/j.topol.2005.08.008 | MR 2243719
[10] Chuan Liu: On weakly bisequential spaces. Comment. Math. Univ. Carolinae 41 (2000), 611–617. MR 1795090
[11] V. I. Malyhin: On countable spaces having no bicompactification of countable tightness. Dokl. Akad. Nauk SSSR 206 (1972), 1407–1411. MR 0320981 | Zbl 0263.54015
[12] E. Michael: A quintuple quotient quest. Gen. Topology Appl. 2 (1972), 91–138. DOI 10.1016/0016-660X(72)90040-2 | MR 0309045 | Zbl 0238.54009
[13] R. C. Olson: Biquotient maps, countably bisequential spaces and related topics. Topology Appl. 4 (1974), 1–28. DOI 10.1016/0016-660X(74)90002-6 | MR 0365463
Search
Partner of
