How to prove $Cone({\bf pt}) \approx D^1,$ and $Cone(D^{n-1}) \approx D^n$ Let $X$ be a topo space. The cone $Cone(X)$ over a topological space $x$ is
the quotient space obtained by identifying all points of the form $(x,1)$ in
the product $(X\times [0,1]$ (supplied with the product topology).i.e $$Cone(X) = (X\times [0,1])/(X\times \{1\}).$$
My question is prove that
(i) $Cone({\bf pt}) \approx D^1,$ where ${\bf pt}$ is one point space.
(ii) $Cone(D^{n-1}) \approx D^n,$ where $D^n = \{x\in \mathbb{R}^n\,\,|\,\,||x||\leqslant 1\}$ is $n$-disk closed.
I don't know how to prove it and I hope, that someone can help. Thank you very much!

Hint: show that in general, any compact convex body with nonempty interior in $\mathbb{R}^n$ is homeomorphic to the closed $n$-disk.
