# 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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