View source for Prüfer surface

An example of a two-dimensional real-analytic manifold (cf. also [[Analytic manifold|Analytic manifold]]) not having a countable basis of open sets. It was introduced in a paper of T. Radó [[#References|[1]]]. There is a generalization of the Prüfer surface to any even dimension (cf. [[#References|[2]]]). However, every [[Riemann surface|Riemann surface]] has a countable basis of open sets (Radó's theorem).

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  T. Radó,   "Ueber den Begriff der Riemannschen Flächen"  ''Acta Szeged'' , '''2'''  (1925)  pp. 101–121</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  E. Calabi,   M. Rosenlicht,   "Complex analytic manifolds without countable base"  ''Proc. Amer. Math. Soc.'' , '''4'''  (1953)  pp. 335–340</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  G. Springer,   "Introduction to Riemann surfaces" , Addison-Wesley  (1957)  pp. Chapt.10</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top">  R. Nevanlinna,   "Uniformisierung" , Springer  (1953)</TD></TR></table>