A Note on Topological Properties of Non-Hausdorff Manifolds
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 t...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/891785 |
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doaj-354710438c7f4f1a8bef953292393ee72020-11-24T22:38:05ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/891785891785A Note on Topological Properties of Non-Hausdorff ManifoldsSteven L. Kent0Roy A. Mimna1Jamal K. Tartir2Department of Mathematics and Statistics, Youngstown State University, One University Plaza, Youngstown, OH 44555, USADepartment of Mathematics and Statistics, Youngstown State University, One University Plaza, Youngstown, OH 44555, USADepartment of Mathematics and Statistics, Youngstown State University, One University Plaza, Youngstown, OH 44555, USAThe 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.http://dx.doi.org/10.1155/2009/891785 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Steven L. Kent Roy A. Mimna Jamal K. Tartir |
| spellingShingle |
Steven L. Kent Roy A. Mimna Jamal K. Tartir A Note on Topological Properties of Non-Hausdorff Manifolds International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Steven L. Kent Roy A. Mimna Jamal K. Tartir |
| author_sort |
Steven L. Kent |
| title |
A Note on Topological Properties of Non-Hausdorff Manifolds |
| title_short |
A Note on Topological Properties of Non-Hausdorff Manifolds |
| title_full |
A Note on Topological Properties of Non-Hausdorff Manifolds |
| title_fullStr |
A Note on Topological Properties of Non-Hausdorff Manifolds |
| title_full_unstemmed |
A Note on Topological Properties of Non-Hausdorff Manifolds |
| title_sort |
note on topological properties of non-hausdorff manifolds |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2009-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2009/891785 |
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