Locally compact perfectly normal spaces may all be paracompact

• Autorzy: Paul B. Larson , Franklin D. Tall
• Języki publikacji: EN

Abstrakty

EN

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 At a crucial step we use some still unpublished results announced by Todorcevic.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 Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space with a hereditarily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.

Kategorie tematyczne

• 03E50: Continuum hypothesis and Martin's axiom
• 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
• 03E65: Other hypotheses and axioms
• 54A25: Cardinality properties (cardinal functions and inequalities, discrete subsets)
• 54D20: Noncompact covering properties (paracompact, Lindel\"of, etc.)
• 54A35: Consistency and independence results
• 03E75: Applications of set theory
• 03E35: Consistency and independence results
• 54D45: Local compactness, σ -compactness
• 54D15: Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 210
• Numer: 3
• Strony: 285-300

Daty

wydano

2010

Twórcy

autor

Paul B. Larson

• Department of Mathematics, Miami University, Oxford, OH 45056, U.S.A.

autor

Franklin D. Tall

• Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada

Identyfikatory

DOI

10.4064/fm210-3-4