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Pach's selection theorem says that there are sets $Z_1 \\subset U_1,\\dots, Z_{d+1} \\subset U_{d+1}$ and a point $u$ in $R^d$ such that each $|Z_i| > c_1(d)n$ and $u$ belongs to $\\langle z_1,...,z_{d+1} \\rangle$ for every choice of $z_1$ in $Z_1,\\dots,z_{d+1}$ in $Z_{d+1}$. Here we show that this theorem does not admit a topological extension with linear size sets $Z_i$. 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Pach's selection theorem says that there are sets $Z_1 \\subset U_1,\\dots, Z_{d+1} \\subset U_{d+1}$ and a point $u$ in $R^d$ such that each $|Z_i| > c_1(d)n$ and $u$ belongs to $\\langle z_1,...,z_{d+1} \\rangle$ for every choice of $z_1$ in $Z_1,\\dots,z_{d+1}$ in $Z_{d+1}$. Here we show that this theorem does not admit a topological extension with linear size sets $Z_i$. 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