Order-Compactifications of Totally Ordered Spaces: Revisited

被引：5
|
作者：
Bezhanishvili, Guram [1 ]
Morandi, Patrick J. [1 ]
机构：
[1] New Mexico State Univ, Dept Math Sci, Las Cruces, NM 88003 USA
来源：
ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2011年 / 28卷 / 03期
关键词：
Ordered topological space; Order-compactification; Totally ordered space; Interval topology; Linearly ordered space; Dedekind-MacNeille completion; LATTICE;
D O I：
10.1007/s11083-010-9193-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Order-compactifications of totally ordered spaces were described by Blatter (J Approx Theory 13: 56-65, 1975) and by Kent and Richmond (J Math Math Sci 11(4): 683-694, 1988). Their results generalize a similar characterization of order-compactifications of linearly ordered spaces, obtained independently by Fedorcuk (Soviet Math Dokl 7: 1011-1014, 1966; Sib Math J 10: 124-132, 1969) and Kaufman (Colloq Math 17: 35-39, 1967). In this note we give a simple characterization of the topology of a totally ordered space, as well as give a new simplified proof of the main results of Blatter (J Approx Theory 13: 56-65, 1975) and Kent and Richmond (J Math Math Sci 11(4): 683-694, 1988). Our main tool will be an order-topological modification of the Dedekind-MacNeille completion. In addition, for a zero-dimensional totally ordered space X, we determine which order-compactifications of X are Priestley order-compactifications.
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页码：577 / 592
页数：16
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