ENGLISH

Regular relations and strictly completely regular ordered spaces

By Xu X. Q. , Liu Y. M.

Book information

Year
2003
Language
english
Format
RAR
Filesize
5 MB (4918898 bytes)
Pages
117\0
Library
mexmat
Time added
2009-07-20 03:45:11

Description

The classical theorem of Zarecki˘ı about regular relations is slightly extended and an intrinsic characterization of regularity is given. Based on the extended Zarecki˘ı theorem and the intrinsic characterization of regularity, we give a characterization of the strict complete regularity of ordered spaces by means of a certain regular relation between the closed and the open upper sets. As an application, it is shown that a quasicontinuous domain endowed with the Lawson topology is strictly completely regular, provided that the Lawson-open lower sets are contained in the lower topology.By means of regular relations we present a new proof of the strict Tychonoff embedding theorem for strictly completely regular ordered spaces.

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