Nonseparated manifolds and completely unstable flows

Abstract

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 ϕ on a Hausdorff (n+1)-manifold E.

Keywords

• completely unstable flows
• nonseparated manifolds
• order structure
• orbit space.