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- Fixed-point_index abstract "In mathematics, the fixed-point index is a concept in topological fixed-point theory, and in particular Nielsen theory. The fixed-point index can be thought of as a multiplicity measurement for fixed points.The index can be easily defined in the setting of complex analysis: Let f(z) be a holomorphic mapping on the complex plane, and let z0 be a fixed point of f. Then the function f(z) − z is holomorphic, and has an isolated zero at z0. We define the fixed point index of f at z0, denoted i(f, z0), to be the multiplicity of the zero of the function f(z) − z at the point z0.In real Euclidean space, the fixed-point index is defined as follows: If x0 is an isolated fixed point of f, then let g be the function defined byThen g has an isolated singularity at x0, and maps the boundary of some deleted neighborhood of x0 to the unit sphere. We define i(f, x0) to be the Brouwer degree of the mapping induced by g on some suitably chosen small sphere around x0.".
- Fixed-point_index wikiPageID "2132356".
- Fixed-point_index wikiPageRevisionID "560387006".
- Fixed-point_index hasPhotoCollection Fixed-point_index.
- Fixed-point_index subject Category:Fixed_points_(mathematics).
- Fixed-point_index subject Category:Topology.
- Fixed-point_index comment "In mathematics, the fixed-point index is a concept in topological fixed-point theory, and in particular Nielsen theory. The fixed-point index can be thought of as a multiplicity measurement for fixed points.The index can be easily defined in the setting of complex analysis: Let f(z) be a holomorphic mapping on the complex plane, and let z0 be a fixed point of f. Then the function f(z) − z is holomorphic, and has an isolated zero at z0.".
- Fixed-point_index label "Fixed-point index".
- Fixed-point_index label "مؤشر النقطة الثابتة".
- Fixed-point_index sameAs m.06p6v7.
- Fixed-point_index sameAs Q5456324.
- Fixed-point_index sameAs Q5456324.
- Fixed-point_index wasDerivedFrom Fixed-point_index?oldid=560387006.
- Fixed-point_index isPrimaryTopicOf Fixed-point_index.