Again, I am reading this.
I am finding it a bit difficult to understand the definition of n-dimensional smooth manifold
.
Now,
$\{U_a; x^1_a, x^2_a, ..., x^n_a\}$ ----(1)
Is the thing (1) a set? (I think it is not).
Is it a tuple?
Also, is $U_a$ a set or a set of sets? What is significance of the subscript $a$?
I would like it very much if someone explains the definition easier to understand. With good examples.