Pinched torus
Definition
The torus pinched at a point, or pinched torus, can be viewed in the following ways:
- It is the one-point compactification of the open cylinder
- It is the quotient of the torus by collapsing one of the sectional circles to a point
- It is the quotient of the sphere by identifying two distinct points
Topological properties
Application of constructs
Covering spaces
The universal covering space of the pinched torus is the pinched helix, which is homotopy-equivalent to a countable wedge of 2-spheres.