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Formalized Mathematics

(a computer assisted approach)

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Volume 20, Issue 1 (Jan 2012)

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Planes and Spheres as Topological Manifolds. Stereographic Projection

Marco Riccardi
  • Via del Pero 102, 54038 Montignoso, Italy
Published Online: 2012-09-12 | DOI: https://doi.org/10.2478/v10037-012-0006-0

Planes and Spheres as Topological Manifolds. Stereographic Projection

The goal of this article is to show some examples of topological manifolds: planes and spheres in Euclidean space. In doing it, the article introduces the stereographic projection [25].

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  • Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.

  • Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990.

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  • Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

  • Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

  • Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

  • Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

  • Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.

  • Agata Darmochwał. Families of subsets, subspaces and mappings in topological spaces. Formalized Mathematics, 1(2):257-261, 1990.

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  • Artur Korniłowicz and Yasunari Shidama. Intersections of intervals and balls in εn/T Formalized Mathematics, 12(3):301-306, 2004.

  • Artur Korniłowicz and Yasunari Shidama. Some properties of circles on the plane. Formalized Mathematics, 13(1):117-124, 2005.

  • Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.

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  • Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.

  • Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

  • Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

  • Mariusz Żynel and Adam Guzowski. T0 topological spaces. Formalized Mathematics, 5(1):75-77, 1996.

About the article


Published Online: 2012-09-12

Published in Print: 2012-01-01



Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-012-0006-0. Export Citation

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