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 Th15:
  for P being Subset of TopSpaceMetr(M) holds P is open iff for p
  being Point of M st p in P ex r being Real st r>0 & Ball(p,r) c= P
by PCOMPS_1:def 4;
