| 词条 | Prüfer manifold |
| 释义 |
In mathematics, the Prüfer manifold or Prüfer surface is a 2-dimensional Hausdorff real analytic manifold that is not paracompact. It was introduced by {{harvtxt|Radó|1925}} and named after Heinz Prüfer. ConstructionThe Prüfer manifold can be constructed as follows {{harv|Spivak|1979|loc=appendix A}}. Take an uncountable number of copies Xa of the plane, one for each real number a, and take a copy H of the upper half plane (of pairs (x, y) with y > 0). Then glue the open upper half of each plane Xa to the upper half plane H by identifying (x,y)∈Xa for y > 0 with the point {{nowrap|(a + yx, y)}} in H. The resulting quotient space Q is the Prüfer manifold. The images in Q of the points (0,0) of the spaces Xa under identification form an uncountable discrete subset. See also
References
2 : Topological spaces|Surfaces |
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