Abstract
We follow [6] and [7] for all terminologies. The purpose of this note is to proveTheorem 1. Let X and Y be any two integer-compact spaces. The following are equivalent:(1)X is homeomorphic to Y.(2)C(X, Z) and C(Y, Z) are isomorphic as rings.(3)C(X, Z) and C(F, Z) are isomorphic as lattices.(4)C(X, Z) and C(Y, Z) are isomorphic as p.o. groups.(5)C(X, Z) and C(Y, Z) are isomorphic as multiplicative semigroups.
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