Difference between revisions of "Prüfer surface"
From Encyclopedia of Mathematics
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| − | 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 | + | An example of a two-dimensional real-analytic manifold (cf. also [[Analytic manifold|Analytic manifold]]) not having a countable basis of open sets. |
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| + | It was introduced in a paper of T. Radó {{Cite|1}}. There is a generalization of the Prüfer surface to any even dimension (cf. {{Cite|2}}). | ||
| + | |||
| + | However, every [[Riemann surface|Riemann surface]] has a countable basis of open sets (Radó's theorem). | ||
====References==== | ====References==== | ||
| − | + | * {{Ref|1}} T. Radó, "Ueber den Begriff der Riemannschen Flächen" ''Acta Szeged'' , '''2''' (1925) pp. 101–121 | |
| + | * {{Ref|2}} E. Calabi, M. Rosenlicht, "Complex analytic manifolds without countable base" ''Proc. Amer. Math. Soc.'' , '''4''' (1953) pp. 335–340 | ||
| + | * {{Ref|3}} G. Springer, "Introduction to Riemann surfaces" , Addison-Wesley (1957) Chap. 10 | ||
| + | * {{Ref|4}} R. Nevanlinna, "Uniformisierung" , Springer (1953) | ||
Latest revision as of 15:05, 30 March 2023
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=32347
Prüfer surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pr%C3%BCfer_surface&oldid=32347
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article