Rings of real-valued functions and the finite subcovering property

Let C be a ring of (not necessarily bounded) real-valued functions with a common domain X such that C includes all the constant functions and if f   and lt; C then | f | ε C

Nonstandard and Standard Compactifications of Ordered Topological Spaces

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

Monads and Realcompactness

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

On bicomplete quasi-pseudometrizability

AbstractWe present a characterization of those quasi-pseudometrizable bitopological spaces which admit a compatible bicomplete quasi-pseudometric. From this result we deduce several generalization, of classical theorems of Alexandroff, Hausdorff, Ĉech and Frolík