
theorem
  for X,Y being non empty TopSpace for d being Function of X, Y holds
  d is relatively_open iff corestr d is open
proof
  let X,Y be non empty TopSpace;
  let d be Function of X, Y;
A1: corestr d = d by WAYBEL18:def 7;
A2: Image d = Y|rng d by WAYBEL18:def 6;
  thus d is relatively_open implies corestr d is open
  by A1,A2;
  assume
A3: for V being Subset of X st V is open holds (corestr d).:V is open;
  let V be open Subset of X;
  thus thesis by A1,A2,A3;
end;
