Locally compact perfectly normal spaces may all be paracompact

Paul B. Larson; Franklin D. Tall

Fundamenta Mathematicae (2010)

  • Volume: 210, Issue: 3, page 285-300
  • ISSN: 0016-2736

Abstract

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 At a crucial step we use some still unpublished results announced by Todorcevic.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 Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space with a hereditarily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

How to cite

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Paul B. Larson, and Franklin D. Tall. "Locally compact perfectly normal spaces may all be paracompact." Fundamenta Mathematicae 210.3 (2010): 285-300. <http://eudml.org/doc/282765>.

@article{PaulB2010,
abstract = {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 At a crucial step we use some still unpublished results announced by Todorcevic.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 Modulo these same unpublished results, we also show that if it is consistent that there is a supercompact cardinal, it is consistent that every locally compact space with a hereditarily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.},
author = {Paul B. Larson, Franklin D. Tall},
journal = {Fundamenta Mathematicae},
keywords = {locally compact; perfectly normal; paracompact; PFA; MA; Suslin tree},
language = {eng},
number = {3},
pages = {285-300},
title = {Locally compact perfectly normal spaces may all be paracompact},
url = {http://eudml.org/doc/282765},
volume = {210},
year = {2010},
}

TY - JOUR
AU - Paul B. Larson
AU - Franklin D. Tall
TI - Locally compact perfectly normal spaces may all be paracompact
JO - Fundamenta Mathematicae
PY - 2010
VL - 210
IS - 3
SP - 285
EP - 300
AB - 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.
LA - eng
KW - locally compact; perfectly normal; paracompact; PFA; MA; Suslin tree
UR - http://eudml.org/doc/282765
ER -

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