Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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 At a crucial step we use some still unpublished results announced by Todorcevic.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 Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space with a hereditarily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.
Słowa kluczowe
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.)
Czasopismo
Rocznik
Tom
Numer
Strony
285-300
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
- Department of Mathematics, Miami University, Oxford, OH 45056, U.S.A.
autor
- Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm210-3-4