We give in this paper additional answers to questions of Lescow and Thomas (A decade of Concurrency, Lecture Notes in Computer Science, Vol. 803, Springer, Berlin, 1994, pp. 583–621), proving topological properties of omega context free languages (ω-CFL) which extend those of O. Finkel (Theoret. Comput. Sci. 262 (1–2) (2001) 669–697): there exist some ω-CFL which are non Borel sets and one cannot decide whether an ω-CFL is a Borel set. We give also an answer to a question of Niwinski (Problem on ω-Powers Posed in the Proceedings of the Workshop “Logics and Recognizable Sets, 1990”) and of Simonnet (Automates et Théorie Descriptive, Ph.D. Thesis, Université Paris 7, 1992) about ω-powers of finitary languages, giving an example of a finitary context free language L such that L^ω is not a Borel set. Then we prove some recursive analogues to preceding properties: in particular one cannot decide whether an ω-CFL is an arithmetical set. Finally we extend some results to context free sets of infinite trees.