منابع مشابه
A Homogeneous Extremally Disconnected Countably Compact Space
It is well known that no infinite homogeneous space is both compact and extremally disconnected. (Since there are infinite compact homogeneous spaces and infinite extremally disconnected homogeneous spaces, it is the combination of compactness and extremal disconnectedness that brings about this result.) The following question then arises naturally: How “close to compact” can a homogeneous, ext...
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We construct a space havfng the properties in the title, and with the same technique, a countably compact T2 topological group which is not absolutely countably compact.
متن کاملOn the product of a compact space with an hereditarily absolutely countably compact space
We show that the product of a compact, sequential T2 space with an hereditarily absolutely countably compact T3 space is hereditarily absolutely countably compact, and further that the product of a compact T2 space of countable tightness with an hereditarily absolutely countably compact ω-bounded T3 space is hereditarily absolutely countably compact.
متن کاملCountably I-compact Spaces
We introduce the class of countably I-compact spaces as a proper subclass of countably S-closed spaces. A topological space (X,T) is called countably I-compact if every countable cover of X by regular closed subsets contains a finite subfamily whose interiors cover X. It is shown that a space is countably I-compact if and only if it is extremally disconnected and countably S-closed. Other chara...
متن کاملPFA(S)[S] and countably compact spaces
We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S)[S]. We also show the consistency without large cardinals of every locally compact, perfectly normal space is paracompact.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1978
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1978-0474206-8