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On the MacNeille Completion of the Category of Partially Ordered Topological Spaces

✍ Scribed by A. Schauerte

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
459 KB
Volume
163
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Preordered topological spaces for which the order has a closed graph form a topological category. Within this category we identify the MacNeille completions (coinciding with the universal initial completions) of five monotopological subcategories, namely those of the T~0~(T~1~, T~2~) preordered spaces and the (completely regular) partially ordered spaces. We also show that a functor due to L. NACHBIN from the quasi‐uniform spaces to the preordered spaces preserves initial sources.

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