Brouwer Fixed Point Theorem in the General Case

Pąk, Karol

doi:10.2478/v10037-011-0024-3

Abstract

In this article we prove the Brouwer fixed point theorem for an arbitrary convex compact subset of εⁿ with a non empty interior. This article is based on [15].

References

Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
Search in Google Scholar
Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
Search in Google Scholar
Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
Search in Google Scholar
Agata Darmochwał. Compact spaces. Formalized Mathematics, 1(2):383-386, 1990.
Search in Google Scholar
Agata Darmochwał. Families of subsets, subspaces and mappings in topological spaces. Formalized Mathematics, 1(2):257-261, 1990.
Search in Google Scholar
Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
Search in Google Scholar
Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Convex sets and convex combinations. Formalized Mathematics, 11(1):53-58, 2003.
Search in Google Scholar
Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Dimension of real unitary space. Formalized Mathematics, 11(1):23-28, 2003.
Search in Google Scholar
Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
Search in Google Scholar
Stanisława Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics, 1(3):607-610, 1990.
Search in Google Scholar
Artur Korniłowicz and Yasunari Shidama. Intersections of intervals and balls in εⁿ/_TFormalized Mathematics, 12(3):301-306, 2004.
Search in Google Scholar
Artur Korniłowicz and Yasunari Shidama. Brouwer fixed point theorem for disks on the plane. Formalized Mathematics, 13(2):333-336, 2005.
Search in Google Scholar
Yatsuka Nakamura, Andrzej Trybulec, and Czesław Byliński. Bounded domains and unbounded domains. Formalized Mathematics, 8(1):1-13, 1999.
Search in Google Scholar
Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
Search in Google Scholar
Karol Sieklucki. Geometria i topologia. PWN, 1979.
Search in Google Scholar
Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
Search in Google Scholar
Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991.
Search in Google Scholar
Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
Search in Google Scholar
Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
Search in Google Scholar
Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Search in Google Scholar
Mirosław Wysocki and Agata Darmochwał. Subsets of topological spaces. Formalized Mathematics, 1(1):231-237, 1990.
Search in Google Scholar

Brouwer Fixed Point Theorem in the General Case

Abstract

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