
theorem Th17:
  for T being non empty TopStruct holds Cl_Seq({}T) = {}
proof
  let T be non empty TopStruct;
  set x = the Element of Cl_Seq({}T);
  assume
A1: Cl_Seq({}T) <> {};
  then x in Cl_Seq({}T);
  then reconsider x as Point of T;
  consider S being sequence of T such that
A2: rng S c= {}T and
  x in Lim S by A1,Def1;
  rng S = {} by A2;
  then dom S = {} by RELAT_1:42;
  hence contradiction by NORMSP_1:12;
end;
