A topological property of Teichmüller spaces (Q1077597)

A subset A in a topological space X is called an open domain if it is the interior of its closure. In this paper it is shown that the Teichmüller space of an arbitrary Fuchsian group is an open domain in the set of bounded holomorphic quadratic differentials for that group. Bounded means in the Bers norm. The result follows easily from a previous result of the author [Sov. Math., Dokl. 21, 252-255 (1980); translation from Dokl. Akad. Nauk SSSR, 250, 1047-1050 (1980; Zbl 0467.30037)]. The theorem has also been proved by Bers and generalizes a result of the reviewer valid only for finite dimensional Teichmüller spaces [Ann. Math. Stud. 97, 3- 5 (1981; Zbl 0458.30031)].