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Full-Text Articles in Physical Sciences and Mathematics
Monads And Realcompactness, Sergio Salbany, Todor D. Todorov
Monads And Realcompactness, Sergio Salbany, Todor D. Todorov
Mathematics
We give a quantifier free characterization of realcompactness and ordered realcompactness in terms of monads. We also present simple proofs of some topological facts concerning realcompact spaces.
Nonstandard And Standard Compactifications Of Ordered Topological Spaces, Sergio Salbany, Todor D. Todorov
Nonstandard And Standard Compactifications Of Ordered Topological Spaces, Sergio Salbany, Todor D. Todorov
Mathematics
We construct the Nachbin ordered compactification and the ordered realcompactification, a notion defined in the paper, of a given ordered topological space as nonstandard ordered hulls. The maximal ideals in the algebras of the differences of monotone continuous functions are completely described. We give also a characterization of the class of completely regular ordered spaces which are closed subspaces of products of copies of the ordered real line, answering a question of T.H. Choe and Y.H. Hong. The methods used are topological (standard) and nonstandard.