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2013 | 11 | 3 | 530-538
Tytuł artykułu

Sequential + separable vs sequentially separable and another variation on selective separability

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EN
Abstrakty
EN
A space X is sequentially separable if there is a countable D ⊂ X such that every point of X is the limit of a sequence of points from D. Neither “sequential + separable” nor “sequentially separable” implies the other. Some examples of this are presented and some conditions under which one of the two implies the other are discussed. A selective version of sequential separability is also considered.
Twórcy
autor
  • Dipartimento di Matematica, Cittá Universitaria, Viale A. Doria 6, 98125, Catania, Italy, bella@dmi.unict.it
Bibliografia
  • [1] Arhangel’skił A.V., Franklin S.P., Ordinal invariants for topological spaces, Michigan Math. J., 1968, 15, 313–320 http://dx.doi.org/10.1307/mmj/1029000034[Crossref]
  • [2] Barman D., Dow A., Selective separability and SS+, Topology Proc., 2011, 37, 181–204
  • [3] Bella A., More on sequential properties of 2ω1, Questions Answers Gen. Topology, 2004, 22(1), 1–4
  • [4] Bella A., Bonanzinga M., Matveev M., Variations of selective separability, Topology Appl., 2009, 156(7), 1241–1252 http://dx.doi.org/10.1016/j.topol.2008.12.029[Crossref]
  • [5] Bella A., Bonanzinga M., Matveev M., Addendum to “Variations of selective separability” [Topology Appl., 156 (7) 2009, 1241–1252], Topology Appl., 2010, 157(15), 2389–2391 http://dx.doi.org/10.1016/j.topol.2010.07.008[Crossref]
  • [6] Bella A., Bonanzinga M., Matveev M.V., Tkachuk V.V., Selective separability: general facts and behavior in countable spaces, In: Spring Topology and Dynamics Conference, Topology Proc., 2008, 32(Spring), 15–30
  • [7] Bella A., Matveev M., Spadaro S., Variations of selective separability II: Discrete sets and the influence of convergence and maximality, Topology Appl., 2012, 159(1), 253–271 http://dx.doi.org/10.1016/j.topol.2011.09.005[WoS][Crossref]
  • [8] van Douwen E.K., The integers and topology, In: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam, 1984, 111–167
  • [9] van Douwen E.K., Applications of maximal topologies, Topology Appl., 1993, 51(2), 125–139 http://dx.doi.org/10.1016/0166-8641(93)90145-4[WoS][Crossref]
  • [10] Dow A., Sequential order under MA, Topology Appl., 2005, 146/147, 501–510 http://dx.doi.org/10.1016/j.topol.2003.09.012[Crossref]
  • [11] Dow A., Vaughan J.E., Ordinal remainders of classical -spaces, Fund. Math., 2012, 217(1), 83–93 http://dx.doi.org/10.4064/fm217-1-7[Crossref]
  • [12] Engelking R., General Topology, Sigma Ser. Pure Math., 6, Heldermann, Berlin, 1989
  • [13] Gartside P., Lo J.T.H., Marsh A., Sequential density, Topology Appl., 2003, 130(1), 75–86 http://dx.doi.org/10.1016/S0166-8641(02)00199-2[Crossref]
  • [14] Gruenhage G., Sakai M., Selective separability and its variations, Topology Appl., 2011, 158(12), 1352–1359 http://dx.doi.org/10.1016/j.topol.2011.05.009[Crossref]
  • [15] Hrušák M., Steprāns J., Cardinal invariants related to sequential separability, In: Axiomatic Set Theory, Kyoto, November 15–17, 2000, Sūrikaisekikenkyūsho Kōkyūroku, 1202, Research Institute for Mathematical Sciences, Kyoto, 2001, 66–74
  • [16] Matveev M., Cardinal p and a theorem of Pelczynski, preprint available at http://arxiv.org/abs/math/0006197
  • [17] Miller A.W., Fremlin D.H., On some properties of Hurewicz, Menger, and Rothberger, Fund. Math., 1988, 129(1), 17–33
  • [18] Scheepers M., Combinatorics of open covers I: Ramsey theory, Topology Appl., 1996, 69(1), 31–62 http://dx.doi.org/10.1016/0166-8641(95)00067-4[Crossref]
  • [19] Scheepers M., Combinatorics of open covers VI: Selectors for sequences of dense sets, Quaest. Math., 1999, 22(1), 109–130 http://dx.doi.org/10.1080/16073606.1999.9632063[Crossref]
  • [20] Tironi G., Isler R., On some problems of local approximability in compact spaces, In: General Topology and its Relations to Modern Analysis and Algebra, III, Prague, August 30–September 3, 1971, Academia, Prague, 1972, 443–446
  • [21] Vaughan J.E., Small uncountable cardinals and topology, In: Open Problems in Topology, North-Holland, Amsterdam, 1990, 195–218
  • [22] Velichko N.V., On sequential separability, Math. Notes, 2005, 78(5–6), 610–614 http://dx.doi.org/10.1007/s11006-005-0164-2[Crossref]
  • [23] Wilansky A., How separable is a space?, Amer. Math. Monthly, 1972, 79(7), 764–765 http://dx.doi.org/10.2307/2316270[Crossref]
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-012-0140-5
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