reserve x,X,X2,Y,Y2 for set;
reserve GX for non empty TopSpace;
reserve A2,B2 for Subset of GX;
reserve B for Subset of GX;

theorem
  for A being Subset of GX st A is connected & A<>{} holds Cl A c=
  Component_of A
proof
  let A be Subset of GX;
  assume that
A1: A is connected and
A2: A<>{};
  Cl A is connected by A1,CONNSP_1:19;
  hence thesis by A1,A2,Th13,PRE_TOPC:18;
end;
