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). | 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==== | ====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> | <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> | ||
Revision as of 11:58, 29 June 2014
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) pp. Chapt.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