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Let S be a sphere in R^n such that S\capQ^n\neq\emptyset and let Cl denotethe closure operator in the Euclidean topology of R^n. If the center of S is inQ^n, then Cl(S\capQ^n) is S, as is easily proved. If the center of S is not inQ^n, then what is Cl(S\capQ^n)? This question, which was answered partially inthe author's paper [Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 7,146--149], is answered completely in this paper by representing Cl(S\capQ^n) interms of the group of Q-automorphisms of the algebraic closure ofQ(\gamma_1,...,\gamma_n) in C, where \gamma_1,...,\gamma_n denote thecoordinates of the center of S.

An algebraic result on the topological closure of the set of rational points on a sphere whose center is non-rational, II