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On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces

Published online by Cambridge University Press:  20 November 2018

Paul Larson  and
Franklin D. Tall
Paul Larson
Affiliation:
Department of Mathematics, Miami University, Oxford, OH 45056 USA e-mail: larsonpb@miamioh.edu
Franklin D. Tall
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 2E4 e-mail: f.tall@utoronto.ca
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Abstract

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We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space that does not include a perfect pre-image of ${{\text{ }\!\!\omega\!\!\text{ }}_{1}}$ is hereditarily paracompact.

Keywords

54D3554D1554D2054D4503E6503E35locally compacthereditarily normalparacompactAxiom RPFA++

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 3 , 01 September 2014 , pp. 579 - 584
Copyright
Copyright © Canadian Mathematical Society 2014

References

[1] Balogh, Z., Locally nice spaces under Martin's axiom. Comment. Math. Univ. Carolin. 24 (1983), no. 1, 63–87.Google Scholar
[2] Balogh, Z., Locally nice spaces and axiom R. Topology Appl. 125 (2002), no. 2, 335–341. http://dx.doi.org/10.1016/S0166-8641(01)00286-3 Google Scholar
[3] Baumgartner, J. E., Applications of the proper forcing axiom. In: Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 913–959.Google Scholar
[4] Burke, D. K., Closed mappings. In: Surveys in general topology, Academic Press, New York-London-Toronto, 1980, pp. 1–32.Google Scholar
[5] Fedorčuk, V. and Hart, K. P., Special constructions. In: Encyclopedia of General Topology, Elsevier, Amsterdam, 2004, pp. 229–232.Google Scholar
[6] Fleissner, W. G., Left separated spaces with point-countable bases. Trans. Amer. Math. Soc. 294 (1986), no. 2, 665–677. http://dx.doi.org/10.1090/S0002-9947-1986-0825729-X Google Scholar
[7] Fischer, A., Tall, F. D., and Todorcevic, S., Forcing with a coherent Souslin tree and locally countable subspaces of countably tight compact spaces., submitted to Topology Appl.Google Scholar
[8] Gruenhage, G., Some results on spaces having an orthobase or a base of subinfinite rank. Proceedings of the 1977 Topology Conference (Louisiana State Univ., Baton Rouge, La., 1977), I. Topology Proc. 2 (1978), no. 1, 151–159.Google Scholar
[9] Hodel, R., Cardinal functions I. In: Handbook of set-theoretic topology. North-Holland, Amsterdam, 1984, pp. 1–61.Google Scholar
[10] Larson, P., An Smax variation for one Souslin tree. J. Symbolic Logic 64 (1999), no. 1, 81–98. http://dx.doi.org/10.2307/2586753 Google Scholar
[11] Larson, P. and Tall, F.D., Locally compact perfectly normal spaces may all be paracompact. Fund. Math. 210 (2010), no. 3, 285–300. http://dx.doi.org/10.4064/fm210-3-4 Google Scholar
[12] Larson, P. and Todorčević, S., Katětov's problem. Trans. Amer. Math. Soc. 354 (2002), no. 5, 1783–1791. http://dx.doi.org/10.1090/S0002-9947-01-02936-1 Google Scholar
[13] Miyamoto, T., !1-Souslin trees under countable support iterations. Fund. Math. 142 (1993), no. 3, 257–261. [14] Z. Szentmikl ´ ossy, S-spaces and L-spaces under Martin's axiom. In: Topology, II, Colloq. Math, Soc. Janos Bolyai, 23, North-Holland, Amsterdam, 1980, pp. 1139–1146.Google Scholar
[15] Tall, F. D., Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems. Dissertationes Math. (Rozprawy Mat.) 148 (1977), 53 pp.Google Scholar
[16] Tall, F. D., PFA(S)[S] : more mutually consistent topological consequences of PFA and V . L. Canad. J. Math. 64 (2012), no. 5, 1182–1200. http://dx.doi.org/10.4153/CJM-2012-010-0 Google Scholar
[17] Tall, F. D., PFA(S)[S] and the Arhangel’skiı-Tall problem. Topology Proc. 40 (2012), 99–108.Google Scholar
[18] Tall, F. D., PFA(S)[S] and locally compact normal spaces. Topology Appl. 162 (2014), 100–115. http://dx.doi.org/10.1016/j.topol.2013.11.012 Google Scholar
[19] Todorcevic, S., Forcing with a coherent Souslin tree. Canad. J. Math., to appear.Google Scholar