Hausdorff property of Manifolds

  • Thread starter hideelo
  • Start date
  • #1
91
14
Is the fact that all manifolds are hausdorff spaces a part of the definition, or can this be proven from the fact that it is a set which is locally isomorphic to open subsets of a hausdorff space?

P.S. if it can be proven I dont want to know the proof, I want to keep working on it, I just want to know that hausdorff property is not some assertion put in from the outset.
 

Answers and Replies

  • #2
pasmith
Homework Helper
1,964
599
The Hausdorff requirement is part of the definition of a topological manifold. There exist non-Hausdorff spaces which are locally homeomorphic to Euclidean spaces.
 
  • Like
Likes hideelo

Related Threads on Hausdorff property of Manifolds

Replies
17
Views
8K
  • Last Post
Replies
1
Views
651
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
3K
Replies
1
Views
2K
Top