zbMATH — the first resource for mathematics

A duality for topological semirings of continuous functions. (English. Russian original) Zbl 0885.46025
Russ. Math. Surv. 51, No. 3, 571-572 (1996); translation from Usp. Mat. Nauk 51, No. 3, 187-188 (1996).
The authors consider topological semigroups of the form \(C_p(X,S)\), where \(S\) is a topological semiring with \(0\) and \(1\), \(0\neq 1\), and \(X\) is an \(S\)-Tikhonov space. For certain semirings \(S\) it is established that the category of the semirings \(C_p(X,S)\) with continuous homomorphism preserving constants is equivalent to the category of the corresponding pairs \((X,S)\). This equivalence generalizes a number of results obtained earlier by Kaplansky, Nagata and Shirota.
46E25 Rings and algebras of continuous, differentiable or analytic functions
54C40 Algebraic properties of function spaces in general topology
54H13 Topological fields, rings, etc. (topological aspects)
Full Text: DOI