Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1996 • Question 14

Question

Math 6510 • Differentiable Manifolds Fall 1996 • Question 14

True or false:

(a) Every local homeomorphism between closed connected manifolds is a covering onto its image.

(b) Every local homeomorphism between open1 1I.e. noncompact and without boundary. connected manifolds is a covering onto its image.

Justify your answers.

Raw LaTeX

True or false:

\textbf{(a)} Every local homeomorphism between closed connected manifolds is a
covering onto its image.

\textbf{(b)} Every local homeomorphism between open\footnote{I.e. noncompact and
without boundary.} connected manifolds is a covering onto its image.

Justify your answers.

Topic Tags

Covering Spaces Homotopy and Degree on Manifolds Smooth Manifolds and Embedded Submanifolds Stokes' Theorem and Integration on Manifolds