  Recently a simple proof of the generalizations of Hawking's black hole
topology theorem and its application to topological black holes for higher
dimensional ($n\geq 4$) spacetimes was given \cite{rnew}. By applying the
associated new line of argument it is proven here that strictly stable
untrapped surfaces do possess exactly the same topological properties as
strictly stable marginally outer trapped surfaces (MOTSs) are known to have. In
addition, a quasi-local notion of outwards and inwards pointing spacelike
directions--applicable to untrapped and marginally trapped surfaces--is also
introduced.
