reserve r for Real;
reserve a, b for Real;
reserve T for non empty TopSpace;
reserve A for non empty SubSpace of T;
reserve P,Q for Subset of T,
  p for Point of T;
reserve M for non empty MetrSpace,
  p for Point of M;
reserve A for non empty SubSpace of M;
reserve F,G for Subset-Family of M;

theorem
  for M being MetrStruct holds the carrier of M = the carrier of
  TopSpaceMetr M & the topology of TopSpaceMetr M = Family_open_set M;
