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]
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. ISBN0-12-634850-2. MR 0575168.
This topology-related article is a stub. You can help Wikipedia by expanding it.
puncture, topology, confused, with, puncturing, coding, theory, topology, puncturing, manifold, removing, finite, points, from, that, manifold, points, small, single, point, this, case, manifold, known, once, punctured, with, removal, second, point, becomes, t. 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 Mobius strip which is a projective plane with a single puncture 2 References edit a b Seifert amp Threlfall 1980 p 29 Seifert amp Threlfall 1980 p 12 Bibliography editSeifert Herbert Threlfall William 1980 A Textbook of Topology Pure and Applied Mathematics Vol 89 Translated by Goldman Michael A New York amp London Academic Press p 12 ISBN 0 12 634850 2 MR 0575168 nbsp This topology related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Puncture topology amp oldid 1217306260, wikipedia, wiki, book, books, library,
