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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2003 • Question 9

Question

Math 6510 • Differentiable Manifolds Fall 2003 • Question 9

Show that every map \(f:S^2\to S^2\) from the 2-sphere to itself admits a point \(x\in S^2\) such that \(f(x)=\pm x\).

Raw LaTeX

Show that every map \(f:S^2\to S^2\) from the 2-sphere to itself admits a point
\(x\in S^2\) such that \(f(x)=\pm x\).

Topic Tags

Fixed Point Theorems and Borsuk-Ulam