Cardinality and structure of semilattices of ordered compactifications

被引：1
|
作者：
Mooney, DD
Richmond, TA
机构：
[1] Department of Mathematics, Western Kentucky University, Bowling Green, Kentucky
来源：
PAPERS ON GENERAL TOPOLOGY AND APPLICATIONS: NINTH SUMMER CONFERENCE AT SLIPPERY ROCK UNIVERSITY | 1995年 / 767卷
关键词：
ordered topological space; completely regular ordered; ordered compactification; lattice; semilattice; cardinality;
D O I：
10.1111/j.1749-6632.1995.tb55906.x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Cardinalities and lattice structures which are attainable by semilattices of ordered compactifications of completely regular ordered spaces are examined. Visliseni and Flachsmeyer have shown that every infinite cardinal is attainable as the cardinality of a semilattice of compactifications of a Tychonoff space. Among the finite cardinals, however, only the Bell numbers are attainable as cardinalities of semilattices of compactifications. It is shown here that all cardinals, both finite and infinite, are attainable as the cardinalities of semilattices of ordered compactifications of completely regular ordered spaces. The last section examines lattice structures which are realizable as semilattices of ordered compactifications, such as chains and power sets.
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页码：188 / 193
页数：6
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