reserve TS for 1-sorted,
  K, Q for Subset of TS;
reserve TS for TopSpace,
  GX for TopStruct,
  x for set,
  P, Q for Subset of TS,
  K , L for Subset of TS,
  R, S for Subset of GX,
  T, W for Subset of GX;

theorem
  R is closed implies Fr R c= R
proof
  assume
A1: R is closed;
  let x be object;
  Cl R = R by A1,PRE_TOPC:22;
  hence thesis by XBOOLE_0:def 4;
end;
