Pinched torus

From Topospaces

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.