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Unformatted text preview: manifold? Is it connected? Repeat the experiment, but this time cutting the M obius band one third of the distance from one of the edges. 4. MTA 3.1-5: Compactication of R n . 5. [Guillemin and Pollack, page 5, #3] Let M , N , and P be smooth manifolds and let f : M N and g : N P be smooth maps. (a) Show that the composite map g f : M P is smooth. (b) Show that if f and g are dieomorphisms, so is g f . (You may use the fact that the composition of smooth functions between open subsets of Euclidian spaces are smooth.) 6. MTA 3.3-1: Graphs of manifolds...
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- Fall '08