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Prüfer manifold
In mathematics, the Prüfer manifold or Prüfer surface is a 2-dimensional Hausdorff real analytic manifold that is not paracompact. It was introduced by and named after Heinz Prüfer.
==Construction==
The Prüfer manifold can be constructed as follows . Take an uncountable number of copies ''X''''a'' 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 each plane ''X''''a'' to the upper half plane ''H'' by identifying (''x'',''y'')∈''X''''a'' for ''y'' > 0 with the point in ''H''. The resulting quotient space is the Prüfer manifold. The images of the points (0,0) in the spaces ''X''''a'' form an uncountable discrete subset.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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