Countable compactness of lexicographic products of GO-spaces

被引：1
作者：
Kemoto, Nobuyuki [1 ]
机构：
[1] Oita Univ, Dept Math, 700 Dannoharu, Oita 8701192, Japan
来源：
COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE | 2019年 / 60卷 / 03期
关键词：
lexicographic product; GO-space; LOTS; countably compact product; PARACOMPACTNESS; NORMALITY;
D O I：
10.14712/1213-7243.2019.020
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We characterize the countable compactness of lexicographic products of GO-spaces. Applying this characterization about lexicographic products, we see: the lexicographic product X-2 of a countably compact GO-space X need not be countably compact, omega(2)(1), omega(1) x omega, (omega + 1) x (omega(1) x 1) x omega(1) x omega, omega(1) x omega x omega(1), omega(1) x omega(1) x omega x omega(1) x omega x center dot center dot center dot, omega(1) omega(omega), omega(1) x omega(omega) x (omega + 1), omega(omega)(1), omega(omega)(1) (omega(1) x 1) and Pi(n epsilon omega) omega(n +1) are countably compact, omega x omega(1) (omega + 1) x (omega(1) x 1) x omega x omega(1), x omega x omega(1) x omega x omega(1) x center dot center dot center dot, omega x omega(omega)(1), omega(1) x omega(omega) x omega(1), omega(omega)(1) x omega, Pi(n epsilon omega) omega(n) and Pi(n <=omega) omega(n +1) are not countably compact, [0, 1)(R) x omega(1), where [0, 1)(R) denotes the half open interval in the real line R, is not countably compact, omega(1) x [0, 1)(R) is countably compact, both S x omega(1) and omega(1) x S are not countably compact, omega(1) x (-omega(1)) is not countably compact, where for a GO-space X = X, <X, TX , -X denotes the GO-space X, >X, TX .
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页码：421 / 439
页数：19
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