reserve a,b,c for set;
reserve r for Real,
  X for set,
  n for Element of NAT;

theorem Th43:
  for X being non empty set, X0 being set for A being proper
  Subset of X0-DiscreteTop(X) holds A is open iff A c= X0
proof
  let X be non empty set, X0 be set;
  let A be proper Subset of X0-DiscreteTop(X);
  A is open iff Int A = A by TOPS_1:23;
  then A is open iff A = A /\ X0 by Th42;
  hence thesis by XBOOLE_1:17,28;
end;
