Closed Mapping - Non-Linear Programming

Hi there

I'm studyin' some mathematics fundamentals for optimizations methods of non-linear programming.

I didn't understood the "Closed Mapping" thing, which is defined in my book ( Luenberg ) like this:

Quote:

A point-to-set mapping A from X to Y is said to be closed at x ∈ X if the assumptions

i) x_k -> x, x_k ∈ X

ii) y_k -> y, y_k ∈ A(x_k)

imply

iii) y ∈ A(x)

The point-to-set map A is said to be closed on X if it is closed at each point of X

I would appreciate any help.