The intermediate value theorem in \(f\)-rings. (English) Zbl 1026.06019
The author investigates in detail three forms of the classical intermediate value theorem for \(f\)-rings, which are lattice-ordered rings that are subdirect products of totally ordered rings. Important examples include the rings \(C(X)\) of continuous functions on completely regular topological spaces \(X\). Several open problems are stated.
Reviewer: M.Droste (Dresden)
MSC:
| 06F25 | Ordered rings, algebras, modules |
| 13J25 | Ordered rings |
| 54C35 | Function spaces in general topology |
| 54C40 | Algebraic properties of function spaces in general topology |
Keywords:
\(F\)-space; semiprime ring; rings of continuous functions; intermediate value theorem; \(f\)-rings; lattice-ordered rings; completely regular topological spacesReferences:
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