Completeness properties of function rings in pointfree topology
Bernhard Banaschewski, Sung Sa Hong (2003)
Commentationes Mathematicae Universitatis Carolinae
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This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or -complete, as lattice ordered rings already hold in the larger setting of pointfree topology. In addition, we prove the corresponding results for rings of integer-valued functions.