Semirings of Continuous (0,∞]-Valued Functions

Resumo

The semiring C^∞(X) of all continuous functions on an arbitrary topological space X with values in the topological semiring (0,∞] is studied. General properties of semirings C^∞(X) are considered. Properties of lattices of ideals and congruences of semirings C^∞(X) over the P-spaces X, the F-spaces X, and the finite discrete spaces are proved.