Puncture (topology)

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), and the Möbius strip (which is a projective plane with a single puncture).

References

Seifert, H. (1980). Seifert and Threlfall, A textbook of topology. W. Threlfall, Joan S. Birman, Julian Eisner. New York: Academic Press. p. 29. ISBN 978-0-12-634850-7. OCLC 316570650.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.

[1] Seifert, H. (1980). Seifert and Threlfall, A textbook of topology. W. Threlfall, Joan S. Birman, Julian Eisner. New York: Academic Press. p. 29. ISBN 978-0-12-634850-7. OCLC 316570650.