Invariance of domain
= Invariance of domain
{wiki}
<Invariance of domain> says that a <continuous map> that is an <injective function> between <topological manifolds> without boundary of the same dimension is an <open map>. It is useful in the <Penrose singularity theorem>: projecting a <compact> <achronal boundary> along timelike curves onto a <Cauchy hypersurface> gives a nonempty subset that is both <open> and <closed>, forcing that <connected> <Cauchy hypersurface> to be <compact>.