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Classifying Spaces - School of Mathematics and Statistics
... B −→ E/G is a well defined, continuous, bijective map with inverse π continuous, i.e. a homeomorphism. ...
... B −→ E/G is a well defined, continuous, bijective map with inverse π continuous, i.e. a homeomorphism. ...
Part1 - Faculty
... Basis of a Topology Let (M ; T) be a topological space. A subset B of the topology T is called a basis of the topology if T contains exactly those sets which result from arbitrary unions of elements of B. Generating set of a Topology A subset E of the power set P(M) is called a generating set on ...
... Basis of a Topology Let (M ; T) be a topological space. A subset B of the topology T is called a basis of the topology if T contains exactly those sets which result from arbitrary unions of elements of B. Generating set of a Topology A subset E of the power set P(M) is called a generating set on ...
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.