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Proceedings of the American Mathematical Society

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Local boundedness and continuity for a functional equation on topological spaces


Author: C. T. Ng
Journal: Proc. Amer. Math. Soc. 39 (1973), 525-529
MSC: Primary 39A40
MathSciNet review: 0318719
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Abstract: It is known that the locally bounded solutions $ f$ of Cauchy's functional equation $ f(x) + f(y) = f(x + y)$ on the reals are necessarily continuous. We shall extend this result to the functional equation $ f(x) + g(y) = h(T(x,y))$ on topological spaces.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0318719-3
Keywords: Functional equations, local boundedness, connected, locally connected, continuous
Article copyright: © Copyright 1973 American Mathematical Society