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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Summer 2018 • Question 5

Question

Math 6510 • Differentiable Manifolds Summer 2018 • Question 5

Let \(M\) and \(N\) be smooth manifolds, and let \(f:M\to N\) be smooth. Prove that the set of all \(p\in M\) for which the differential \(D_pf:T_pM\to T_{f(p)}N\) is injective is an open set.

Raw LaTeX

Let \(M\) and \(N\) be smooth manifolds, and let \(f:M\to N\) be smooth. Prove
that the set of all \(p\in M\) for which the differential
\(D_pf:T_pM\to T_{f(p)}N\) is injective is an open set.

Topic Tags

Differential Forms and Exterior Calculus Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds