reserve S, R for 1-sorted,
  X for Subset of R,
  T for TopStruct,
  x for set;
reserve H for non empty multMagma,
  P, Q, P1, Q1 for Subset of H,
  h for Element of H;
reserve G for Group,
  A, B for Subset of G,
  a for Element of G;

theorem Th49:
  for G being BinContinuous TopGroup, O being open Subset of G, a
  being Element of G holds a * O is open
proof
  let G be BinContinuous TopGroup, O be open Subset of G, a be Element of G;
  a * O = (a*).:O by Th15;
  hence thesis by Th24;
end;
