论文信息 - f-Rings and the Stone-Weierstrass Theorem

f-Rings and the Stone-Weierstrass Theorem

Using an appropriate notion of separating subring, it is shown that the classical Stone-Weierstrass Theorem for compact Hausdorff spaces is ultimately a result about f-rings. As an application the constructively valid Stone-Weierstrass Theorem for compact completely regular frames is obtained.

Bernhard Banaschewski | B. Banaschewski

[1] S. Vickers. Topology via Logic , 1989 .

[2] B. Banaschewski,et al. Lattice Aspects of Radical Ideals and Choice Principles , 1985 .

[3] M. Henriksen. A Survey of f-Rings and Some of their Generalizations , 1997 .

[4] Klaus Keimel,et al. Groupes et anneaux réticulés , 1977 .

[5] Leonard Gillman,et al. Rings of continuous functions , 1961 .

[6] Bernhard Banaschewski,et al. A constructive proof of the Stone-Weierstrass theorem , 1997 .