Punctured_plane

Puncture (topology)

Puncture (topology)

Removal of points from a manifold

Not to be confused with Puncturing (coding theory).

In topology, puncturing a manifold is removing a finite set of points from that manifold.[1] 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),[1] and the Möbius strip (which is a projective plane with a single puncture).[2]

References

  1. [1]
    Seifert & Threlfall 1980, p. 29.
  2. [2]
    Seifert & Threlfall 1980, p. 12.

Bibliography

  • Seifert, Herbert; Threlfall, William (1980). A Textbook of Topology. Pure and Applied Mathematics. Vol. 89. Translated by Goldman, Michael A. New York & London: Academic Press. p. 12. ISBN 0-12-634850-2. MR 0575168.


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