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2012 | 20 | 2 | 97-104
Tytuł artykułu

Fundamental Group of n-sphere for n ≥ 2

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Triviality of fundamental groups of spheres of dimension greater than 1 is proven, [17]
Słowa kluczowe
Wydawca
Rocznik
Tom
20
Numer
2
Strony
97-104
Opis fizyczny
Daty
wydano
2012-12-01
online
2013-02-02
Twórcy
  • Via del Pero 102, 54038 Montignoso, Italy
  • Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok, Poland
Bibliografia
  • [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [4] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  • [5] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [6] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [7] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [8] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [9] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  • [10] Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991.
  • [11] Adam Grabowski. Introduction to the homotopy theory. Formalized Mathematics, 6(4):449-454, 1997.
  • [12] Adam Grabowski and Artur Korniłowicz. Algebraic properties of homotopies. FormalizedMathematics, 12(3):251-260, 2004.
  • [13] Artur Korniłowicz. The fundamental group of convex subspaces of En T. Formalized Mathematics, 12(3):295-299, 2004.
  • [14] Artur Korniłowicz. On the isomorphism of fundamental groups. Formalized Mathematics, 12(3):391-396, 2004.
  • [15] Artur Korniłowicz and Yasunari Shidama. Intersections of intervals and balls in En T. Formalized Mathematics, 12(3):301-306, 2004.
  • [16] Artur Korniłowicz, Yasunari Shidama, and Adam Grabowski. The fundamental group. Formalized Mathematics, 12(3):261-268, 2004.
  • [17] John M. Lee. Introduction to Topological Manifolds. Springer-Verlag, New York Berlin Heidelberg, 2000.
  • [18] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • [19] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.
  • [20] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
  • [21] Marco Riccardi. The definition of topological manifolds. Formalized Mathematics, 19(1):41-44, 2011, doi: 10.2478/v10037-011-0007-4.[Crossref]
  • [22] Marco Riccardi. Planes and spheres as topological manifolds. Stereographic projection. Formalized Mathematics, 20(1):41-45, 2012, doi: 10.2478/v10037-012-0006-0.[Crossref]
  • [23] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [24] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [25] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-012-0013-1
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