reserve T for TopStruct;
reserve GX for TopSpace;

theorem Th18:
  for A being Subset of T holds A c= Cl A
proof
  let A be Subset of T;
  now
    let x be object;
    assume
A1: x in A;
    assume not x in Cl A;
    then ex C being Subset of T st C is closed & A c= C & not x in C by A1,Th15
;
    hence contradiction by A1;
  end;
  hence thesis;
end;
