Locally Compact Perfectly Normal Spaces May All Be Paracompact
نویسندگان
چکیده
Using results announced by Stevo Todorcevic we establish that if it is consistent that there is a supercompact cardinal then it is consistent that every locally compact perfectly normal space is paracompact. Modulo the large cardinal, this answers a question of S. Watson. We also solve a problem raised by the second author, proving that it is consistent with ZFC that every first countable hereditarily normal countable chain condition space is hereditarily separable. Finally, we 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.
منابع مشابه
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