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Difference between revisions of "Prüfer surface"

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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 [[#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).
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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.
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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}}).
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However, every [[Riemann surface|Riemann surface]] has a countable basis of open sets (Radó's theorem).
  
 
====References====
 
====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>
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* {{Ref|1}} T. Radó, "Ueber den Begriff der Riemannschen Flächen"  ''Acta Szeged'' , '''2'''  (1925)  pp. 101–121
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* {{Ref|2}} E. Calabi, M. Rosenlicht, "Complex analytic manifolds without countable base"  ''Proc. Amer. Math. Soc.'' , '''4'''  (1953)  pp. 335–340
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* {{Ref|3}} G. Springer, "Introduction to Riemann surfaces" , Addison-Wesley  (1957)  Chap. 10
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* {{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=13767
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article