Good time of day. I have the following question. It's written in wiki in examples of CAT($k$) spaces (https://en.wikipedia.org/wiki/CAT(k)_space) that the closed subspace $X$ of $\mathbb E^3$ (where $\mathbb E^3$ is a 3-dimensional Euclidean space) given by $X=\mathbb E^3 \setminus \{(x,y,z)|x>0, y>0, z>0\}$ equipped with the induced length metric is not a CAT($k$) space for any $k$.
I want to understand why it's true.
If you don't mind can you please explain this question in more details?
Thank you!