theorem Th66:
  for B being non empty Subset of TOP-REAL n, A being Subset of
  TOP-REAL n,a being Real st A={q: |.q.|=a} & A`=B holds
  (TOP-REAL n) | B is locally_connected
proof
  let B be non empty Subset of TOP-REAL n, A be Subset of TOP-REAL n,a be Real;
  assume
A1: A={q: |.q.|=a} & A`=B;
  then A` is open by Th64;
  hence thesis by A1,Th65;
end;
