Let $U_0$ := (-1/10.1/10) and $U_a$ := (a/2,2) for 0 < a < 1. Show that $U_0$$\cup${$U_a$ : 0 < a < 1} is an open cover of [0, 1]. Find a Lebesgue number of this cover.
I don't know how to find a lebsgue number since my book has no example how to find lebsgue number. I have read the theorem and it's proof. But i dont understand how to find the number. I have proved that given open cover actually covers [0,1]. Since if x$\in$[0,1] and x=0 or 1 then x$\in$$U_0$or $U_1$ and if x is in (0,1) then x is <1/10 or x>1/10 or x=1/10. For this cases x belongs to $U_0$ or $U_{1/5}$ or $U_{1/10}$.
