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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Spring 2016 • Question 12

Question

Math 6510 • Differentiable Manifolds Spring 2016 • Question 12

Prove that if \(U\subseteq \mathbb {R}^n\) and \(V\subseteq \mathbb {R}^m\) are open, nonempty, and homeomorphic, then \(n=m\).

Raw LaTeX

Prove that if \(U\subseteq\R^n\) and \(V\subseteq\R^m\) are open, nonempty, and
homeomorphic, then \(n=m\).

Topic Tags

Smooth Manifolds and Embedded Submanifolds