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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1997 • Question 4

Question

Math 6510 • Differentiable Manifolds Fall 1997 • Question 4

Prove that \(\mathbb {R}^n\) is not homeomorphic to \(\mathbb {R}^k\) for \(k\ne n\). (Do not appeal to Brouwer’s invariance of domain theorem.)

Raw LaTeX

Prove that \(\mathbb{R}^n\) is not homeomorphic to \(\mathbb{R}^k\) for
\(k\ne n\). (Do not appeal to Brouwer's invariance of domain theorem.)

Topic Tags

Smooth Manifolds and Embedded Submanifolds