Microbundles (Ex)

Exercise 0.1 Milnor1964.

1. Let $M$$<wikitex>; {{beginthm|Exercise|Milnor1964|Lemma 2.1, Theorem 2.2}} # Let $M$ be a topological manifold. Show that $\xi_M : = (M \times M, M, \Delta_M, p_1)$ is a micro bundle. # Let $M$ be a smooth manifold. Show that $TM$ and $\xi_M$ are isomorphic micro bundles. {{endthm}} </wikitex> == References == {{#RefList:}} [[Category:Exercises]] [[Category:Exercises without solution]]M$ be a topological manifold. Show that $\xi_M : = (M \times M, M, \Delta_M, p_1)$$\xi_M : = (M \times M, M, \Delta_M, p_1)$ is a micro bundle.
2. Let $M$$M$ be a smooth manifold. Show that $TM$$TM$ and $\xi_M$$\xi_M$ are isomorphic micro bundles.