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International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 4, Pages 745-756
http://dx.doi.org/10.1155/S016117128700084X

Nonseparated manifolds and completely unstable flows

University of Houston-Downtown, Houston, Texas 77002, USA

Received 18 August 1986

Copyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.