In 2005, Dijkstra studied subspaces $\mathscr{E}$ of the Banach spaces $\ell^p$ that are constructed as `products' of countably many zero-dimensional subsets of $\bm{R}$ , as a generalization of Erdös space and complete Erdös space. He presented a criterion for deciding whether a space of the type $\mathscr{E}$ has the same peculiar features as Erdös space, which is one-dimensional yet totally disconnected and has a one-dimensional square. In this paper, we extend the construction to a nonseparable setting and consider spaces $\mathscr{E}_\mu$ corresponding to products of $\mu$ zero-dimensional subsets of $\bm{R}$ in nonseparable Banach spaces. We are able to generalize both Dijkstra's criterion and his classification of closed variants of $\mathscr{E}$ . We can further generalize the latter to complete spaces and we find that a one-dimensional complete space $\mathscr{E}_\mu$ is homeomorphic to a product of complete Erdös space with a countable product of discrete spaces. Among the applications, we find coincidence of the small and large inductive dimension for $\mathscr{E}_\mu$ .