Planes and Spheres as Topological Manifolds. Stereographic Projection

Marco Riccardi

Formalized Mathematics (2012)

  • Volume: 20, Issue: 1, page 41-45
  • ISSN: 1426-2630

Abstract

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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].

How to cite

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Marco Riccardi. "Planes and Spheres as Topological Manifolds. Stereographic Projection." Formalized Mathematics 20.1 (2012): 41-45. <http://eudml.org/doc/267814>.

@article{MarcoRiccardi2012,
abstract = {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].},
author = {Marco Riccardi},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {41-45},
title = {Planes and Spheres as Topological Manifolds. Stereographic Projection},
url = {http://eudml.org/doc/267814},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Marco Riccardi
TI - Planes and Spheres as Topological Manifolds. Stereographic Projection
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 1
SP - 41
EP - 45
AB - 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].
LA - eng
UR - http://eudml.org/doc/267814
ER -

References

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  1. Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990. 
  2. Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  3. Grzegorz Bancerek. König's theorem. Formalized Mathematics, 1(3):589-593, 1990. 
  4. Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  5. Grzegorz Bancerek. Monoids. Formalized Mathematics, 3(2):213-225, 1992. 
  6. Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  7. Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990. 
  8. Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  9. Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  10. Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  11. Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  12. Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  13. Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990. 
  14. Agata Darmochwał. Families of subsets, subspaces and mappings in topological spaces. Formalized Mathematics, 1(2):257-261, 1990. 
  15. Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. 
  16. Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. 
  17. Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991. 
  18. Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  19. Katarzyna Jankowska. Matrices. Abelian group of matrices. Formalized Mathematics, 2(4):475-480, 1991. 
  20. Stanisława Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics, 1(3):607-610, 1990. 
  21. Artur Korniłowicz and Yasunari Shidama. Intersections of intervals and balls in εn/T Formalized Mathematics, 12(3):301-306, 2004. 
  22. Artur Korniłowicz and Yasunari Shidama. Some properties of circles on the plane. Formalized Mathematics, 13(1):117-124, 2005. 
  23. Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  24. Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990. 
  25. John M. Lee. Introduction to Topological Manifolds. Springer-Verlag, New York Berlin Heidelberg, 2000. Zbl0956.57001
  26. Robert Milewski. Bases of continuous lattices. Formalized Mathematics, 7(2):285-294, 1998. 
  27. Yatsuka Nakamura, Artur Korniłowicz, Nagato Oya, and Yasunari Shidama. The real vector spaces of finite sequences are finite dimensional. Formalized Mathematics, 17(1):1-9, 2009, doi:10.2478/v10037-009-0001-2.[Crossref] 
  28. Henryk Oryszczyszyn and Krzysztof Prażmowski. Real functions spaces. Formalized Mathematics, 1(3):555-561, 1990. Zbl0916.51004
  29. Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990. 
  30. Beata Padlewska. Locally connected spaces. Formalized Mathematics, 2(1):93-96, 1991. 
  31. Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990. 
  32. Karol Pąk. Basic properties of metrizable topological spaces. Formalized Mathematics, 17(3):201-205, 2009, doi: 10.2478/v10037-009-0024-8.[Crossref] 
  33. Marco Riccardi. The definition of topological manifolds. Formalized Mathematics, 19(1):41-44, 2011, doi: 10.2478/v10037-011-0007-4.[Crossref] Zbl1276.57023
  34. Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990. 
  35. Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003. 
  36. Wojciech A. Trybulec. Basis of real linear space. Formalized Mathematics, 1(5):847-850, 1990. 
  37. Wojciech A. Trybulec. Linear combinations in real linear space. Formalized Mathematics, 1(3):581-588, 1990. 
  38. Wojciech A. Trybulec. Subspaces and cosets of subspaces in real linear space. Formalized Mathematics, 1(2):297-301, 1990. 
  39. Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  40. Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  41. Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  42. Mariusz Żynel and Adam Guzowski. T0 topological spaces. Formalized Mathematics, 5(1):75-77, 1996. 

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