reserve m,n,i,i2,j for Nat,
  r,r1,r2,s,t for Real,
  x,y,z for object;
reserve p,p1,p2,p3,q,q1,q2,q3,q4 for Point of TOP-REAL n;
reserve u for Point of Euclid n;
reserve R for Subset of TOP-REAL n;
reserve P,Q for Subset of TOP-REAL n;

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;
