Simplicial Complexes
... the set of vertices of τ is a subset of the set of vertices of σ. A face of σ is said to be a proper face if it is not equal to σ itself. An r-dimensional face of σ is referred to as an r-face of σ. A 1-dimensional face of σ is referred to as an edge of σ. Note that any simplex is a face of itself. ...
... the set of vertices of τ is a subset of the set of vertices of σ. A face of σ is said to be a proper face if it is not equal to σ itself. An r-dimensional face of σ is referred to as an r-face of σ. A 1-dimensional face of σ is referred to as an edge of σ. Note that any simplex is a face of itself. ...
Topology I with a categorical perspective
... modern, categorical point of view. There are a number of reasons this alternative can be better. Since many students are familiar with point-set ideas already, they are in a good position to learn something new about these ideas, like the universal properties characterizing them. Plus, using categor ...
... modern, categorical point of view. There are a number of reasons this alternative can be better. Since many students are familiar with point-set ideas already, they are in a good position to learn something new about these ideas, like the universal properties characterizing them. Plus, using categor ...
3-manifold
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.