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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. Ourresult is that an ordered nonseparated n-manifold X can be realized as an ordered orbit space of a completely unstable continuous flow ϕ on a Hausdorff (n+1)-manifold E

Nonseparated manifolds and completely unstable flows