A Homogeneous Extremally Disconnected Countably Compact Space
نویسندگان
چکیده
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, extremally disconnected space be? The aim of this paper is to show that a homogeneous extremally disconnected space can be countably compact. It is shown also, assuming Martin’s Axiom, that there exist countably compact, homogeneous, extremally disconnected spaces whose product is not countably compact.
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