I'm having some problems finding the topology for the Baire space .

This is what I've found in one book:

http://i50.tinypic.com/2qtwr6f.jpg,

and this is what I've found in another one:

http://i46.tinypic.com/29mr5zr.jpg.

My question is, are these two topologies the same?

That is, are the sets and the sets the same, for ?

Thank you.