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Aug 28, 2013 at 5:25 comment added Misha @MarcPalm: In this case, any proper analytic subset $A\subset U$ (one just should not denote it $U$ as OP does) is discrete and the decomposition is $A=A_1$: All connected components of $A$ are points, and, hence, irreducible.
Aug 27, 2013 at 15:29 comment added Marc Palm For $U$ upper halfplane and $\Gamma$ Fuchsian, can you give an example? I don't see it.
Aug 27, 2013 at 14:46 history asked mmm CC BY-SA 3.0