Let \mathcal A=(A,V_A,v) be an n-dimensional affine space with the associated normed vector space (V_A,||~||) over the field of real numbers \mathbb R). Let P_0,P_1,P_2\ldots,P_s be s,\, (s\le n) affinely independent points. A non-empty subset \mathcal U\subset \mathcal B of the affine subspace. \mathcal B:=\{\lambda_0P_0+\cdots+\lambda_sP_s\,:\,\lambda_i\in \mathbb R, \,i=0,\ldots,s\,\wedge\, \lambda_0+\cdots+\lambda_s=1\}
with the designated barycenter. B:=\{\lambda(P_0+\cdots+P_s)\,:\,\lambda:=(s+1)^{-1}\in \mathbb R\}\in\mathcal U
is called bounded, if there exists an upper bound c\in\mathbb R with
||\overrightarrow{BQ}||\le c
for all Q\in\mathcal U.
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