Geodesic
Completeness properties of function rings in pointfree topology
Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 2, pp. 245-259

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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 $\sigma$-comp\-lete, 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.
This note establishes that the familiar internal characterizations of the Tychonoff spaces whose rings of continuous real-valued functions are complete, or $\sigma$-comp\-lete, 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.
Classification : 06D22, 54C30, 54G05
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 
Banaschewski, Bernhard; Hong, Sung Sa. Completeness properties of function rings in pointfree topology. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) no. 2, pp. 245-259. http://geodesic.mathdoc.fr/item/CMUC_2003_44_2_a5/
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     author = {Banaschewski, Bernhard and Hong, Sung Sa},
     title = {Completeness properties of function rings in pointfree topology},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {245--259},
     year = {2003},
     volume = {44},
     number = {2},
     mrnumber = {2026162},
     zbl = {1098.06006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2003_44_2_a5/}
}
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