Nonseparated manifolds and completely unstable flows (Q1091651)

We define an order structure on a nonseparated n-manifold. Here, a nonseparated manifold denotes any topological space that is locally Euclidean and has a countable basis; the usual Hausdorff separation property is not required. Our result is that an ordered nonseparated n- manifold X can be realized as an ordered orbit space of a completely unstable continuous flow \(\phi\) on a Hausdorff \((n+1)\)-manifold E.