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The real numbers in pointfree topology. (English) Zbl 0891.54009
Textos de Matemática. Série B. 12. Coimbra: Universidade de Coimbra, Departamento de Matemática, 94 p. (1997).
This paper, reporting a series of lectures, is basically an exposition of “\(C(X)\) theory” in frames/locales. It is a careful exposition, not constructive but almost entirely conducted in ZF without choice. The last three sections, on realcompactness/strong realcompactness, on Stone-Weierstrass theorems, and (using countable choice) on \(\sigma\)-frames/Alexandroff algebras, are more than careful: innovative exposition (with some technically new results).

54C30 Real-valued functions in general topology
06D20 Heyting algebras (lattice-theoretic aspects)
18B25 Topoi
26B99 Functions of several variables
54B30 Categorical methods in general topology
54C05 Continuous maps