Let \(\ell\) and -u be upper semicontinuous bounded functions on [a,b] with \(\ell \leq u\). For H being an n-dimensional subspace of C[a,b] let \(K=\{p\in H:\ell \leq p\leq u\}\). This paper characterizes K for which card K\(=0\) or 1 or \(\infty\), where card K denotes the cardinality of K.