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Notes - WVU Math Department
... Definition 1 An incidence plane is any triple hP, L, Fi, where sets P and L are disjoint and F is a binary relation from P to L. The elements of P are typically referred to as points, while the elements of L are typically referred to as lines. The relation hP, `i ∈ F is usually (but not always) inte ...
... Definition 1 An incidence plane is any triple hP, L, Fi, where sets P and L are disjoint and F is a binary relation from P to L. The elements of P are typically referred to as points, while the elements of L are typically referred to as lines. The relation hP, `i ∈ F is usually (but not always) inte ...
3-manifold
![](https://commons.wikimedia.org/wiki/Special:FilePath/3-Manifold_3-Torus.png?width=300)
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.