In this article a conformal compactification of the space R^3 x S^1 is obtained, (§2) . In §3 a decay property of the curvature is given, and in §4 the maximum principle is applied and we discuss removable singularities. In §3, 4 we depend heavily on the elaborated works by Uhlenbeck, [2] , [4]. The result of this article is used to study symmetry breaking at infinity [3].