reserve C for Simple_closed_curve,
  i, j, n for Nat,
  p for Point of TOP-REAL 2;

theorem Th17:
  for C being closed Subset of TOP-REAL 2, p being Point of Euclid
  2 st p in BDD C ex r being Real st r > 0 & Ball(p,r) c= BDD C
proof
  let C be closed Subset of TOP-REAL 2, p be Point of Euclid 2;
  set W = Int BDD C;
  assume p in BDD C;
  then p in W by TOPS_1:23;
  then consider r being Real such that
A1: r > 0 and
A2: Ball(p,r) c= BDD C by GOBOARD6:5;
  reconsider r as Real;
  take r;
  thus thesis by A1,A2;
end;
