Brouwer Fixed Point Theorem in the General Case

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Brouwer Fixed Point Theorem in the General Case

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].

Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.

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

Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

Agata Darmochwał. Compact spaces. Formalized Mathematics, 1(2):383-386, 1990.

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

Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.

Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Convex sets and convex combinations. Formalized Mathematics, 11(1):53-58, 2003.

Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Dimension of real unitary space. Formalized Mathematics, 11(1):23-28, 2003.

Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.

Stanisława Kanas, Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics, 1(3):607-610, 1990.

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

Artur Korniłowicz and Yasunari Shidama. Brouwer fixed point theorem for disks on the plane. Formalized Mathematics, 13(2):333-336, 2005.

Yatsuka Nakamura, Andrzej Trybulec, and Czesław Byliński. Bounded domains and unbounded domains. Formalized Mathematics, 8(1):1-13, 1999.

Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.

Karol Sieklucki. Geometria i topologia. PWN, 1979.

Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.

Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991.

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

Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

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

Mirosław Wysocki and Agata Darmochwał. Subsets of topological spaces. Formalized Mathematics, 1(1):231-237, 1990.

Formalized Mathematics

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SCImago Journal Rank (SJR) 2016: 0.207
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researchers in the fields of formal methods and computer-checked mathematics

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