On subsets of \(\mathbb{C}^{n+1}\) in general position (Q1924882)

Let \(X\) be a subset of \(\mathbb{C}^{n+1}\) in general position. We say \(X\) is maximal if for any \(Y\) in general position contained in \(\mathbb{C}^{n+1}\) for which \(X\subset Y\), then \(X=Y\). Furthermore if \(X\) is maximal and the elements of \(X\cap\{x_{n+1}=0\}\) is \(\nu\), then we say \(X\) is \(\nu\)-maximal. In the first part of this paper, the author proves the existence of a \(\nu\)-maximal subset in \(\mathbb{C}^{n+1}\) for any \(\nu\) with \(1\leq\nu\leq n\). The author also raises a question: Is there any 0-maximal subset of \(\mathbb{C}^{n+1}\) for \(n\geq 2\)? In the second part of this paper, the author generalizes the theorems in the first part to the set of holomorphic curves.