ag.algebraic geometry - complement of "good reduction" points in p-adic shimura varieties

gn.common topology – Is it workable to show that surfaces with compact border are homeomorphic by glueing disks to the border elements? Answer

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gn.common topology – Is it workable to show that surfaces with compact border are homeomorphic by glueing disks to the border elements?

Let $S_1$ and $S_2$ breathe two surfaces with compact border and $M_1$ and $M_2$ the surfaces obtained by glueing closed disks to the border of $S_1$ and $S_2$, respectively. Is there a direct proof that if $M_1$ and $M_2$ are homeomorphic then $S_1$ and $S_2$ are too homeomorphic? I do know that this will breathe finished within the compact illustration utilizing regular figure, as in Massey’s bespeak. And if the surfaces aren’t any compact?

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