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Local boundedness and continuity for a functional equation on topological spaces. (English) Zbl 0272.39009


MSC:

39B52 Functional equations for functions with more general domains and/or ranges
39B05 General theory of functional equations and inequalities
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[1] J. Aczél, Lectures on functional equations and their applications, Mathematics in Science and Engineering, Vol. 19, Academic Press, New York-London, 1966. Translated by Scripta Technica, Inc. Supplemented by the author. Edited by Hansjorg Oser. · Zbl 0139.09301
[2] M. G. Darboux, Sur le théorème fondamental de la géométrie projective, Math. Ann. 17 (1880), no. 1, 55 – 61 (French). · JFM 12.0447.02 · doi:10.1007/BF01444119
[3] J. L. Denny, Cauchy’s equation and sufficient statistics on arcwise connected spaces, Ann. Math. Statist. 41 (1970), 401 – 411. · Zbl 0201.18604 · doi:10.1214/aoms/1177697079
[4] C. T. Ng, On the functional equation \( f(x) + \sum\nolimits_{i = 1}^n {{g_i}({y_i}) = h(T(x,{y_1},{y_2}, \cdots ,{y_n}))} \), Ann. Polon. Math. 27 (to appear). · Zbl 0227.39005
[5] J. Pfanzagl, On a functional equation related to families of exponential probability measures, Aequationes Math. 4 (1970), 139 – 142. · Zbl 0194.45302 · doi:10.1007/BF01817754
[6] -, On the functional equation \( \varphi (x) + \varphi (y) = \psi (T(x,y))\), Aequationes Math. 6 (1970), 202-205.
[7] Raymond Louis Wilder, Topology of Manifolds, American Mathematical Society Colloquium Publications, vol. 32, American Mathematical Society, New York, N. Y., 1949. · Zbl 0039.39602
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