On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces
Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 579-584

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2014-010-3
Mots-clés : 54D35, 54D15, 54D20, 54D45, 03E65, 03E35, locally compact, hereditarily normal, paracompact, Axiom R, PFA++
Larson, Paul; Tall, Franklin D. On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces. Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 579-584. doi: 10.4153/CMB-2014-010-3
@article{10_4153_CMB_2014_010_3,
     author = {Larson, Paul and Tall, Franklin D.},
     title = {On the {Hereditary} {Paracompactness} of {Locally} {Compact,} {Hereditarily} {Normal} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {579--584},
     year = {2014},
     volume = {57},
     number = {3},
     doi = {10.4153/CMB-2014-010-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-010-3/}
}
TY  - JOUR
AU  - Larson, Paul
AU  - Tall, Franklin D.
TI  - On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces
JO  - Canadian mathematical bulletin
PY  - 2014
SP  - 579
EP  - 584
VL  - 57
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-010-3/
DO  - 10.4153/CMB-2014-010-3
ID  - 10_4153_CMB_2014_010_3
ER  - 
%0 Journal Article
%A Larson, Paul
%A Tall, Franklin D.
%T On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces
%J Canadian mathematical bulletin
%D 2014
%P 579-584
%V 57
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-010-3/
%R 10.4153/CMB-2014-010-3
%F 10_4153_CMB_2014_010_3

[1] [1] Balogh, Z., Locally nice spaces under Martin's axiom. Comment. Math. Univ. Carolin. 24 (1983), no. 1, 63–87. Google Scholar

[2] [2] Balogh, Z., Locally nice spaces and axiom R. Topology Appl. 125 (2002), no. 2, 335–341. Google Scholar | DOI

[3] [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] [4] Burke, D. K., Closed mappings. In: Surveys in general topology, Academic Press, New York-London-Toronto, 1980, pp. 1–32. Google Scholar

[5] [5] Fedorčuk, V. and Hart, K. P., Special constructions. In: Encyclopedia of General Topology, Elsevier, Amsterdam, 2004, pp. 229–232. Google Scholar

[6] [6] Fleissner, W. G., Left separated spaces with point-countable bases. Trans. Amer. Math. Soc. 294 (1986), no. 2, 665–677. Google Scholar | DOI

[7] [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] [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] [9] Hodel, R., Cardinal functions I. In: Handbook of set-theoretic topology. North-Holland, Amsterdam, 1984, pp. 1–61. Google Scholar

[10] [10] Larson, P., An Smax variation for one Souslin tree. J. Symbolic Logic 64 (1999), no. 1, 81–98. Google Scholar | DOI

[11] [11] Larson, P. and Tall, F.D., Locally compact perfectly normal spaces may all be paracompact. Fund. Math. 210 (2010), no. 3, 285–300. Google Scholar | DOI

[12] [12] Larson, P. and Todorčević, S., Katětov's problem. Trans. Amer. Math. Soc. 354 (2002), no. 5, 1783–1791. Google Scholar | DOI

[13] [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] [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] [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. Google Scholar | DOI

[17] [17] Tall, F. D., PFA(S)[S] and the Arhangel’skiı-Tall problem. Topology Proc. 40 (2012), 99–108. Google Scholar

[18] [18] Tall, F. D., PFA(S)[S] and locally compact normal spaces. Topology Appl. 162 (2014), 100–115. Google Scholar | DOI

[19] [19] Todorcevic, S., Forcing with a coherent Souslin tree. Canad. J. Math., to appear. Google Scholar

Cité par Sources :