International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 891785, 4 pages
doi:10.1155/2009/891785
A note on topological properties of non-Hausdorff manifolds
Steven L. Kent
, Roy A. Mimna
and Jamal K. Tartir
Department of Mathematics and Statistics, Youngstown State University, One University Plaza, Youngstown, OH 44555, USA
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.