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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2017 • Question 12

Question

Math 6510 • Differentiable Manifolds Summer 2017 • Question 12

Let \(D^n\) be a closed \(n\)-dimensional disk. Prove that if \(f\) is a homeomorphism of \(D^n\), then \(f\) fixes some \(x\in D^n\).

Raw LaTeX

Let \(D^n\) be a closed \(n\)-dimensional disk. Prove that if \(f\) is a
homeomorphism of \(D^n\), then \(f\) fixes some \(x\in D^n\).

Topic Tags

Smooth Manifolds and Embedded Submanifolds