Prüfer surface
From HandWiki
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).
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)
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