Bernhard Banaschewski, Sung Sa Hong
Completeness properties of function rings in pointfree topology

Comment.Math.Univ.Carolinae 44,2 (2003) 245-259.

Abstract:This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or $\sigma $-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.

Keywords: frame of reals, lattice ordered rings of real valued continuous functions and integer valued continuous functions, extremally disconnected frame, basically disconnected frame, cozero map
AMS Subject Classification: 06D22, 54C30, 54G05