reserve a, b, c, d, r, s for Real,
  n for Element of NAT,
  p, p1, p2 for Point of TOP-REAL 2,
  x, y for Point of TOP-REAL n,
  C for Simple_closed_curve,
  A, B, P for Subset of TOP-REAL 2,
  U, V for Subset of (TOP-REAL 2)|C`,
  D for compact with_the_max_arc Subset of TOP-REAL 2;

theorem Th41:
  for T being non empty TopSpace, a being Point of T holds
  I[01] --> a is Path of a,a
proof
  let T be non empty TopSpace, a be Point of T;
  thus a,a are_connected;
  thus thesis by BORSUK_1:def 14,def 15,TOPALG_3:4;
end;
