Puncture (topology)

In topology, puncturing a manifold is removing a finite set of points from that manifold.Template:Sfn The set of points can be small as a single point. In this case, the manifold is known as once-punctured. With the removal of a second point, it becomes twice-punctured, and so on.

Examples of punctured manifolds include the open disk (which is a sphere with a single puncture), the cylinder (which is a sphere with two punctures),Template:Sfn and the Möbius strip (which is a projective plane with a single puncture).Template:Sfn

The set of non-zero complex numbers is the complex plane once punctured at the origin, sometimes denoted ${ℂ}^{\ast }$.

Bibliography

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