No, B has to be open. And in which case, A isone ofP's neighbourhoods.

No established radius. This definition only holds for metric spaces.b) "Set V is a neighborhood of point P if a small disk around P is contained in V" - Wikipedia. What is this small disk? Is it a set? Is there an established radius?

It's more commonly called a ball

By the way, in Wikipedia, they talk about a ball, not a disk...