# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Locally compact perfectly normal spaces may all be paracompact

### Tom 210 / 2010

Fundamenta Mathematicae 210 (2010), 285-300 MSC: Primary 54D15, 54D20, 54D45, 03E35, 54A35; Secondary 03E50, 03E65, 03E75, 54A20, 54A25. DOI: 10.4064/fm210-3-4

#### Streszczenie

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 At a crucial step we use some still unpublished results announced by Todorcevic.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 Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space with a hereditarily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

#### Autorzy

• Paul B. LarsonDepartment of Mathematics
Miami University
Oxford, OH 45056, U.S.A.
e-mail
• Franklin D. TallDepartment of Mathematics
University of Toronto