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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.
##### MSC:
 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)
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