Analytic structure of $q$-pseudoconcave subsets of continuous graphs

Let $Z\subset {\mathbb{C}}^N$ be an $n$-pseudoconcave subset, for $1\le n<N$, which is locally the graph of a continuous function over a closed subset of ${\mathbb{C}}^n\times \mathbb{R}$. We show that $Z$ can be realised as the disjoint union of $n$-dimensional complex manifolds. In particular, the same conclusion can be made for any $n$-pseudoconcave subset $Z$ of the graph $\mathrm{\Gamma }(g)$ of a continuous function $g:D\subset {\mathbb{C}}^n\times \mathbb{R}\to \mathbb{R}\times {\mathbb{C}}^p$, for $n\ge 1$ and $p\ge 0$.