Displaying similar documents to “C- and C*-quotients in pointfree topology”

Archimedean frames, revisited

Jorge Martinez (2008)

Commentationes Mathematicae Universitatis Carolinae

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This paper extends the notion of an archimedean frame to frames which are not necessarily algebraic. The new notion is called and is . Assuming the Axiom of Choice and for compact normal algebraic frames, the new and the old coincide. There is a subfunctor from the category of compact normal frames with skeletal maps with joinfit values, which is almost a coreflection. Conditions making it so are briefly discussed. The concept of an element arises naturally, and the join of suitably...

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 σ -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.