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Summary Of: Brouwer fixed point theorem

In three dimensions the consequence of the Brouwer fixed point theorem is that no matter how much you stir or shake a cocktail in a glass... The Brouwer fixed point theorem was one of the early achievements of... This is equivalent to the Brouwer fixed point theorem for dimension 2... The Brouwer fixed point theorem forms the starting point of a number of more general... The generalizations of the Brouwer fixed point theorem to infinite dimensional spaces therefore all include a compactness assumption of some sort... generalizes the Brouwer fixed point theorem in a different direction... the Brouwer fixed point theorem can be generalized to arbitrary...

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mathematics | fixed point theorem | L. E. J. Brouwer | continuous function | closed unit ball | fixed point | integer | Euclidean n-space | bijective | surjective | homeomorphisms | closed | connected | without holes | Banach fixed point theorem | contraction mapping | algebraic topology | fixed point theorems | functional analysis | Piers Bohl | L. E. J. Brouwer | Jacques Hadamard | indirect proofs | intuitionist | boundary | sphere | | | retraction | codomain | fundamental groups | group homomorphism | vector fields | homology groups | cyclic | combinatorial proof | Sperner's lemma | indirect proof | Weierstrass approximation theorem | Sard's theorem | David Gale | Hex | determinacy | fixed point theorems | Hilbert space | compact | 2 | convexity | fixed point theorems in infinite-dimensional spaces | Kakutani fixed point theorem | semi-continuous | correspondences | forcing | cardinals | cardinality | Lefschetz fixed-point theorem | singular homology | Sperner's lemma | Borsuk-Ulam theorem | Tucker's lemma | Topological combinatorics | Encyclopaedia of Mathematics | ISBN 978-1556080104 | doi | cut-the-knot | PlanetMath | Categories | Fixed points | Continuous mappings | Mathematical theorems |
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