Question: 4.1. Let n be a positive integer. Let X be an n-manifold. Show that X admits an open covering {Ui C X}ier together with homeomorphisms

4.1. Let n be a positive integer. Let X be an n-manifold. Show that X admits an open covering {Ui C X}ier together with homeomorphisms di: Ui - R" for all i E I. 4.2. Let S be a surface with boundary (as defined in class). Show that S admits an open covering {Vj C S}jes together with homeomorphisms v; of Vi with R2 or R x R>0

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