Prüfer surface

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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 [1]. There is a generalization of the Prüfer surface to any even dimension (cf. [2]). However, every Riemann surface has a countable basis of open sets (Radó's theorem).


[1] T. Radó, "Ueber den Begriff der Riemannschen Flächen" Acta Szeged , 2 (1925) pp. 101–121
[2] E. Calabi, M. Rosenlicht, "Complex analytic manifolds without countable base" Proc. Amer. Math. Soc. , 4 (1953) pp. 335–340
[3] G. Springer, "Introduction to Riemann surfaces" , Addison-Wesley (1957) pp. Chapt.10
[4] R. Nevanlinna, "Uniformisierung" , Springer (1953)
How to Cite This Entry:
Prüfer surface. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article