let P=$\{(x,sin x) \in \mathbb R^2\} $
I need to find with respect to the euclidean metric ,d.
a open cover of P that has a finite sub cover
a open cover that does not have a finite sub cover
a $d_{P}$ open cover.
for the last part I'm thinking I can just take arcs of the curve.
for the first one can I just take all points to the left of y axis and all points to the right of x axis so the union covers and it's finite so I can take that as finite sub cover?
and for the second would union of rectangles of width one height 2 do?