Suppose that S is a smooth surface a) Show that there exist smooth parametrizations (j, Ej) of portions of S such that S UNj 1 j(Ej) b) Show that there exist nonoverlapping surfaces Sj with smooth parametrizations such that S UNj 1 Sj What happens if S is orientable ...

a By definition given x S there is a parametrization x E x which is smooth at x ie such tha ...

Suppose that S is a smooth surface. a) Show that there exist smooth parametrizations (j, Ej) of

Question:

Suppose that S is a smooth surface.
a) Show that there exist smooth parametrizations (ϕj, Ej) of portions of S such that S = UNj=1 ϕj(Ej).
b) Show that there exist nonoverlapping surfaces Sj with smooth parametrizations such that S = UNj=1 Sj. What happens if S is orientable?