Copyright © 2009 Steven L. Kent et al. 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

The notion of compatible apparition points is introduced for non-Hausdorff manifolds, and properties of these points are studied. It is well known that the Hausdorff property is independent of the other conditions given in the standard definition of a topological manifold. In much of literature, a topological manifold of dimension n is a Hausdorff topological space which has a countable base of open sets and is locally Euclidean of dimension n. We begin with the definition of a non-Hausdorff topological manifold.