In a more specific example,

let A={$\displaystyle 0<(x^2)+(y^2)<=1$} where A is a subset of $\displaystyle R^2$

let Lim(A) be the set of all limit points of A (I am assumingthis is what Lim(A) means btw)

is Lim(A)={$\displaystyle 0<=(x^2)+(y^2)<=1$} where Lim(A) is a subset of $\displaystyle R^2$?

but then the closure of A, Cl(A)=Lim(A) which makes me question my understanding of the definition of limit points...or is that right?

Intuitively, I think of Lim(A)={0} union {$\displaystyle x^2$+$\displaystyle y^2$=1} which is actually Bd(A)