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On The Generalized Cauchy Equation

Published online by Cambridge University Press:  20 November 2018

Itrel Monroe
Itrel Monroe*
Affiliation:
University of Florida, Gainesville
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It is the purpose of this note to prove the following theorem: Let ƒ: G → R be a non-constant continuous function with G a locally compact connected topological group and with R the real numbers. Let C = ƒ(G) and suppose that F: C × C → C is a junction such that

Then ƒ is monotone and open and F is continuous.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 1314 - 1318
Copyright
Copyright © Canadian Mathematical Society 1967

References

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