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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
frame of reals; lattice ordered rings of real valued continuous functions and integer valued continuous functions; extremally disconnected frame; basically disconnected frame; cozero map
Summary:
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.
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