A curious example involving ordered compactifications

Applied General Topology

Thomas A. Richmond¹ 

[1] Western Kentucky University;

关键词: Ordered topological space;    Ordered compactification;    Galois connection;    Quasi-uniformity;    F-poset;   

DOI  :  10.4995/agt.2002.2064

来源: DOAJ

【 摘 要 】

For a certain product X x Y where X is compact, connected, totally ordered space, we find that the semilattice K0 (X x Y) of ordered compactifications of X x Y is isomorphic to a collection of Galois connections and to a collection of functions F which determines a quasi-uniformity on an extended set X U {+∞}, from which the topology and order on X is easily recovered. It is well-known that each ordered compactification of an ordered space X x Y corresponds to a totally bounded quasi-uniformity on X x Y compatible with the topology  and order on X x Y, and thus K0 (X x Y) may be viewed as a collection of quasi-uniformities on X x Y. By the results here, these quasi-uniformities on X x Y determine a quasi-uniformity on the related space X U {+∞}.

【 授权许可】

Unknown