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On the MacNeille Completion of the Category of Partially Ordered Topological Spaces
Author(s) -
Schauerte A.
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931630123
Subject(s) - mathematics , functor , topological space , pure mathematics
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.