Summary: Let \(C\) denote the Banach space of real-valued continuous functions on \([0,1]\). Let \({\Phi}: C\times C\to C\). If \({\Phi} \in \{ +,\min ,\max\}\), then \({\Phi}\) is an open mapping but the multiplication \({\Phi} = \cdot\) is not open. For an open ball \(B(f,r)\) in~\(C\), let \(B^2(f,r) = B(f,r) \cdot B(f,r)\). Then \(f^2 \in\operatorname {Int}B^2(f,r)\) for all \(r>0\) if and only if either \(f \geq 0\) on \([0,1]\) or \(f \leq 0\) on \([0,1]\). Another result states that \(\operatorname{Int} (B_1 \cdot B_2) \neq \emptyset\) for any two balls \(B_1\) and~\(B_2\) in~\(C\). We also prove that if \({\Phi} \in \{+,\cdot,\min,\max\}\), then the set \({\Phi}^{-1}(E)\) is residual whenever \(E\) is residual in~\(C\).