An example of a two-dimensional real-analytic manifold (cf. also Analytic manifold) not having a countable basis of open sets. It was introduced in a paper of T. Radó . There is a generalization of the Prüfer surface to any even dimension (cf. ). However, every Riemann surface has a countable basis of open sets (Radó's theorem).
|||T. Radó, "Ueber den Begriff der Riemannschen Flächen" Acta Szeged , 2 (1925) pp. 101–121|
|||E. Calabi, M. Rosenlicht, "Complex analytic manifolds without countable base" Proc. Amer. Math. Soc. , 4 (1953) pp. 335–340|
|||G. Springer, "Introduction to Riemann surfaces" , Addison-Wesley (1957) pp. Chapt.10|
|||R. Nevanlinna, "Uniformisierung" , Springer (1953)|
Prüfer surface. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Pr%C3%BCfer_surface&oldid=32347