Czes Kosniowski: Homeomorphic topological spaces $S^{1}\times I / \sim$ and $D^{2}$ Let $X=S^1\times I$ where $S^1\subset \mathbb{C}$ and $I=[0,1]\subset \mathbb{R}$ also define the equivalence relation ~ by $(x,t)$~$(y,s)$ if and only if $xt=ys$.   Prove that $X$/~ is homeomorphic to the unit disc $D^2=\{x\in \mathbb{R^2}: |x|\le1\}=\{x\in \mathbb{C}: |x|\le1\}$ with the induced topology.  Any hints would be appreciated.
$(S^1 \times [0,1])/\sim$ homeomorphic to unit disk $ D^2$ Let $\sim$ be the equivalence relation on $S_1 \times I$ given by $(x,t)\sim(y,s)$ if and only if $xt=ys$ where $I=[0,1]$  How do I prove that $(S_1 \times I)/\sim$ is homeomorphic to the unit disk $D^2$ with the induced topology?
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