I think I have been stuck on this question for too long and I really need to know how to rigorously solve this:
Let $K=(V,S)$ be a finite Simplicial complex and let $p$ be an element not included in $V$ . We define $CK=(V∪{p}), CS)$ , $ CS$ being equal to ${a∪{p},a∈S}$ .
QUESTION: Prove that the geometric realization of $CK $is homeomorphic to the cone on the geometric realization of $K$ .
Thank you for the help!