consider x being object such that
A1: x in the carrier of T by XBOOLE_0:def 1;
reconsider x = x as Point of (TopSpaceMetr T) by A1;
reconsider f = S --> x as Function of S,(TopSpaceMetr T) ;
f in { f where f is Function of S,(TopSpaceMetr T) : f is continuous } ;
hence { f where f is Function of S,(TopSpaceMetr T) : f is continuous } is non empty set ; :: thesis: verum