## 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

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