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 Th3:
  R is closed iff R` is open
proof
  R is closed iff [#] GX \ R is open by PRE_TOPC:def 3;
  hence thesis;
end;
