![Exercise Sheet 11 - D-MATH](http://s1.studyres.com/store/data/000798130_1-0a63e5cfa44cf2db092cced444a855bf-300x300.png)
Lecture 5 and 6
... d) for all U ∈ U0 and x ∈ E there is an ε > 0, so that λx ∈ U , for all λ ∈ K with |λ| < ε , e) if (E, T ) is Hausdorff, then for every x ∈ E, x (= 0, there is a U ∈ U0 with x (∈ U , f ) if E is locally convex, then there is for all U ∈ U0 a convex V ∈ U0 , with V ⊂ U , i.e. 0 has a neighborhood bas ...
... d) for all U ∈ U0 and x ∈ E there is an ε > 0, so that λx ∈ U , for all λ ∈ K with |λ| < ε , e) if (E, T ) is Hausdorff, then for every x ∈ E, x (= 0, there is a U ∈ U0 with x (∈ U , f ) if E is locally convex, then there is for all U ∈ U0 a convex V ∈ U0 , with V ⊂ U , i.e. 0 has a neighborhood bas ...
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.