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International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 891785, 4 pages
http://dx.doi.org/10.1155/2009/891785
Research Article

A Note on Topological Properties of Non-Hausdorff Manifolds

Department of Mathematics and Statistics, Youngstown State University, One University Plaza, Youngstown, OH 44555, USA

Received 26 September 2008; Revised 11 February 2009; Accepted 29 June 2009

Academic Editor: Francois Goichot

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.