Previous |  Up |  Next

Article

Full entry | Fulltext not available (moving wall 24 months)      Feedback
Keywords:
linearly H-closed space; normal space; first countable space; forcing axiom
Summary:
We use topological consequences of {\sf PFA}, {\sf MA$_{\omega_1}$(S)[S]} and {\sf PFA(S)[S]} proved by other authors to show that normal first countable linearly H-closed spaces with various additional properties are compact in these models.
References:
[1] Abraham U., Todorčević S.: Martin's axiom and first-countable $S$- and $L$-spaces. Handbook of Set-theoretic Topology, North-Holland, Amsterdam, 1984, pages 327–346. MR 0776627
[2] Alas O. T., Junqueira L. R., Wilson R. G.: On linearly H-closed spaces. Topology Appl. 258 (2019), 161–171. DOI 10.1016/j.topol.2019.02.014 | MR 3924509
[3] Baillif M.: Notes on linearly H-closed spaces and OD-selection principles. Topology Proc. 54 (2019), 109–124. MR 3892579
[4] Balogh Z., Dow A., Fremlin D. H., Nyikos P. J.: Countable tightness and proper forcing. Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 1, 295–298. DOI 10.1090/S0273-0979-1988-15649-2 | MR 0940491
[5] Balogh Z., Gruenhage G.: Two more perfectly normal non-metrizable manifolds. Topology Appl. 151 (2005), no. 1–3, 260–272. DOI 10.1016/j.topol.2003.12.021 | MR 2139756
[6] Bella A.: Observations on some cardinality bounds. Topology Appl. 228 (2017), 355–362. DOI 10.1016/j.topol.2017.06.007 | MR 3679094
[7] Dow A., Tall F. D.: PFA(S)[S] and countably compact spaces. available in ArXiv 1607.04368 [math.LO] (2016), 24 pages. MR 3702781
[8] Eisworth T., Nyikos P., Shelah S.: Gently killing S-spaces. Israel J. Math. 136 (2003), 189–220. DOI 10.1007/BF02807198 | MR 1998110
[9] Larson P. B., Tall F. D.: Locally compact perfectly normal spaces may all be paracompact. Fund. Math. 210 (2010), no. 3, 285–300. DOI 10.4064/fm210-3-4 | MR 2733053
[10] Larson P., Tall F. D.: On the hereditary paracompactness of locally compact, hereditarily normal spaces. Canad. Math. Bull. 57 (2014), no. 3, 579–584. DOI 10.4153/CMB-2014-010-3 | MR 3239121
[11] Nyikos P.: The theory of nonmetrizable manifolds. Handbook of Set-theoretic Topology, North-Holland, Amsterdam, 1984, pages 633–684. MR 0776633
[12] Nyikos P. J.: Applications of some strong set-theoretic axioms to locally compact $T_5$ and hereditarily scwH spaces. Fund. Math. 176 (2003), no. 1, 25–45. DOI 10.4064/fm176-1-3 | MR 1971471
[13] Porter J. R., Woods R. G.: Feebly compact spaces, Martin's axiom and “diamond”. Proc. of the 1984 Topology Conf., Auburn, Ala., 1984, Topology Proc. 9 (1984), no. 1, 105–121. MR 0781555
[14] Roitman J.: Basic $S$ and $L$. Handbook of Set-theoretic Topology, North-Holland, Amsterdam, 1984, pages 295–326. MR 0776626 | Zbl 0594.54001
[15] Szentmiklóssy Z.: $S$-spaces and $L$-spaces under Martin's axiom. Topology, Vol. II, Proc. Fourth Colloq., Budapest, 1978, Colloq. Math. Soc. János Bolyai, 23, North-Holland, Amsterdam, 1980, pages 1139–1145. MR 0588860
[16] Tall F. D.: PFA(S)[S] and the Arhangel'skiĭ–Tall problem. Topology Proc. 40 (2012), 99–108. MR 2817292
[17] Tall F. D.: PFA(S)[S] for the masses. Topology Appl. 232 (2017), 13–21. DOI 10.1016/j.topol.2017.09.033 | MR 3720876
[18] Todorčević S.: Partition Problems in Topology. Contemporary Mathematics, 84, American Mathematical Society, Providence, 1989. DOI 10.1090/conm/084 | MR 0980949
Partner of
EuDML logo