# Prüfer surface

From Encyclopedia of Mathematics

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).

#### References

- [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) Chap. 10
- [4] R. Nevanlinna, "Uniformisierung" , Springer (1953)

**How to Cite This Entry:**

Prüfer surface.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Pr%C3%BCfer_surface&oldid=53547

This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article