Semi-homogeneous functions
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- by Louis V. Quintas and Fred Supnick PDF
- Proc. Amer. Math. Soc. 14 (1963), 620-625 Request permission
References
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The special case $p(a) = a\;(a \in A \subset R)$ was first considered by the authors and the results announced in Abstract 577-8, Notices Amer. Math. Soc. 8 (1961), 51.
If $0 \in A$ and $p \equiv 1$, then $C(1,A)$ is the set of all constant functions. If $0 \ni A$, A is not null, and $p \equiv 1$ on ${A^\ast }$, then $C(1,A)$ is the set of all functions which are constant on the cosets of ${R^\ast }/{A^\ast }$ and $f(0)$ is an arbitrary constant.
- Georg Hamel, Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung: $f(x+y)=f(x)+f(y)$, Math. Ann. 60 (1905), no. 3, 459–462 (German). MR 1511317, DOI 10.1007/BF01457624 By a decomposition of a set X we mean a disjoint family of subsets of X whose union is X.
- Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869 H. Steinhaus, A new property of G. Cantor’s set, Wektor 7 (1917). (Polish) See also, J. F. Randolph, Distances between points of the Cantor set, Amer. Math. Monthly 47 (1940), 549.
Additional Information
- © Copyright 1963 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 14 (1963), 620-625
- MSC: Primary 39.30
- DOI: https://doi.org/10.1090/S0002-9939-1963-0155117-3
- MathSciNet review: 0155117