= Circle modulo reflection
{title2=$S^1/(z\sim\overline z)\cong[0,1]$}
Identify points of the <circle> having the same real coordinate, equivalently points related by <complex conjugation>. The <continuous> <surjection> $h(z)=(1+\operatorname{Re}z)/2$ has exactly these <equivalence classes> as its fibers. It induces a <continuous bijection> from the <quotient space> to the <closed interval>. The <quotient space> is <compact> as a <continuous image of a compact space>, while the <closed interval> is <Hausdorff>, so the <compact-to-Hausdorff continuous bijection theorem> makes the induced map a <homeomorphism>. The two fixed points of the reflection become the two interval endpoints.
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