Hereditarily paracompact and compact monotonically normal spaces
نویسندگان
چکیده
منابع مشابه
Monotonically Compact and Monotonically Lindelöf Spaces
We answer questions of Bennett, Lutzer, and Matveev by showing that any monotonically compact LOTS is metrizable, and any first-countable Lindelöf GO-space is monotoncically Lindelöf. We also show that any compact monotonically Lindelöf space is first-countable, and is metrizable if scattered, and that separable monotonically compact spaces are metrizable.
متن کاملLocally Compact Perfectly Normal Spaces May All Be Paracompact
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 hered...
متن کاملCompact-calibres of Regular and Monotonically Normal Spaces
A topological space has calibre ω1 (resp., calibre (ω1,ω)) if every point-countable (resp., point-finite) collection of nonempty open sets is countable. It has compact-calibre ω1 (resp., compact-calibre (ω1,ω)) if, for every family of uncountably many nonempty open sets, there is some compact set which meets uncountably many (resp., infinitely many) of them. It has CCC (resp., DCCC) if every di...
متن کاملOn the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces
We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space which does not include a perfect pre-image of ω1 is hereditarily paracompact. This is the fifth in a series of papers ([LTo], [L2], [FTT], [LT], [T1] being the logically previous ones) that establish powerful topological consequences in models ...
متن کاملCompact Monotonically Metacompact Spaces Are Metrizable
Monotonically metacompact spaces were recently introduced as an extension of the concept of monotonically compact spaces. In this note we answer a question of Popvassilev, and Bennett, Hart, and Lutzer, by showing that every compact, Hausdorff, monotonically (countably) metacompact space is metrizable. We also show that certain countable spaces fail to be monotonically (countably) metacompact.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2001
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(99)00136-4