R^2 accumulation and open/closed

[Dustinsfl]

All points $(x,y)$ such that $x^2 - y^2 < 1$.

This set is open but I am not sure about the accumulation points.

 

[CaptainBlack]

All points $(x,y)$ such that $x^2 - y^2 < 1$.

This set is open but I am not sure about the accumulation points.

The set is the region of \(\mathbb{R}^2\) between the branches of the hyperbola \(x^2-y^2=1\). All the points on the hyperbola are accumulation points, so the set of accumulation points is \( \{(x,y)\in \mathbb{R}^2: x^2-y^2\le 1 \}\)

CB