Elementary functional equations on partially ordered linear algebra

Dai, Taen Yu

doi:10.1090/S0002-9939-1980-0565331-0

Elementary functional equations on partially ordered linear algebra
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Proc. Amer. Math. Soc. 79 (1980), 167-173 Request permission

Abstract:

Suppose that a Dedekind $\sigma$-complete partially ordered linear algebra A admits a function with familiar functional and order properties as possessed by the real-valued exponential, logarithm, root or power function on the real line. Then A can be characterized as an algebra of almost finite extended-real-valued continuous functions defined on some proper topological space.

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