![PDF](http://s1.studyres.com/store/data/008798931_1-a8faedae10f28777398670b4d4380718-300x300.png)
2: THE NOTION OF A TOPOLOGICAL SPACE Part of the rigorization
... with at least two points) is not metrizable. Thus the class of topological spaces up to homeomorphism is more general than the class of metric spaces up to homeomorphism. On the other hand, there are times when having a metric is more convenient than just a topology. For this and other reasons it is ...
... with at least two points) is not metrizable. Thus the class of topological spaces up to homeomorphism is more general than the class of metric spaces up to homeomorphism. On the other hand, there are times when having a metric is more convenient than just a topology. For this and other reasons it is ...
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.