
theorem Th10:
  for T being TopStruct, B being Basis of T, S being Subset of T
  st S in B holds S is open
proof
  let T be TopStruct, B be Basis of T, S be Subset of T such that
A1: S in B;
  B c= the topology of T by TOPS_2:64;
  hence thesis by A1;
end;
