Locally compact perfectly normal spaces may all be paracompact

Paul B. Larson¹ ; Franklin D. Tall²

¹ Department of Mathematics Miami University Oxford, OH 45056, U.S.A.
² Department of Mathematics University of Toronto Toronto, Ontario M5S 2E4, Canada

Fundamenta Mathematicae, Tome 210 (2010) no. 3, pp. 285-300

Résumé

We work towards establishing that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. At a crucial step we use some still unpublished results announced by Todorcevic. Modulo this and the large cardinal, this answers a question of S. Watson. Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space with a hereditarily normal square is metrizable. We also solve a problem raised by the second author, proving it consistent with ZFC that every first countable hereditarily normal countable chain condition space is hereditarily separable.

Détail

DOI : 10.4064/fm210-3-4

Keywords: work towards establishing consistent there supercompact cardinal consistent every locally compact perfectly normal space paracompact crucial step still unpublished results announced todorcevic modulo large cardinal answers question watson modulo these unpublished results consistent there supercompact cardinal consistent every locally compact space hereditarily normal square metrizable solve problem raised second author proving consistent zfc every first countable hereditarily normal countable chain condition space hereditarily separable