๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Strictly complete regularity of the Lawson topology on a continuous poset

โœ Scribed by Xiao-Quan Xu


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
63 KB
Volume
103
Category
Article
ISSN
0166-8641

No coin nor oath required. For personal study only.

โœฆ Synopsis


For a continuous poset P , let ฯ‰(P ) and ฮป(P ) be the lower topology and the Lawson topology on P , respectively. In this paper, we constructively prove in the set theory ZFDC ฯ‰ (the theory obtained by adjoining the axiom of ฯ‰ dependent choices to the Zermelo-Fraenkel set theory) that if all lower closed subsets in (P , ฮป(P )) are closed in (P , ฯ‰(P )), then (P , ฮป(P )) is a strictly completely regular ordered space.


๐Ÿ“œ SIMILAR VOLUMES