I'm trying to prove that $\overline{st_K(x)}$ is a cone on $lk_K(x)$, but can't seem to get anywhere!
I know how to construct a topological cone given a space $X$. However I don't know any way to test whether a space is a cone on another space. Could someone give me a hint for this, and possibly outline some methods I might employ in the future for similar problems?
Many thanks!