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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2017 • Question 11

Question

Math 6510 • Differentiable Manifolds Spring 2017 • Question 11

Prove that nonempty open subsets of \(\mathbb {R}^m\) and \(\mathbb {R}^n\) are not homeomorphic if \(m\ne n\).

Raw LaTeX

Prove that nonempty open subsets of \(\R^m\) and \(\R^n\) are not
homeomorphic if \(m\ne n\).

Topic Tags

Smooth Manifolds and Embedded Submanifolds