
theorem
  for T being injective T_0-TopSpace holds T is compact locally-compact sober
proof
  let T be injective T_0-TopSpace;
  set S = the Scott TopAugmentation of Omega T;
A1: S is compact locally-compact sober by WAYBEL14:32;
  the TopStruct of S = the TopStruct of T by Th37;
  hence thesis by A1,YELLOW14:26,27,28;
end;
