
theorem Th26:
  for X being non empty compact TopSpace
  for F being Point of C_Normed_Algebra_of_ContinuousFunctions X holds
  ||.F.|| = 0 implies F = 0.C_Normed_Algebra_of_ContinuousFunctions X
proof
  let X be non empty compact TopSpace;
  let F be Point of C_Normed_Algebra_of_ContinuousFunctions X;
  reconsider F1 = F
    as Point of C_Normed_Algebra_of_BoundedFunctions the carrier of X by Lm1;
  (||.F1.|| = 0 iff F1
     = 0.(C_Normed_Algebra_of_BoundedFunctions the carrier of X)) by CC0SP1:25;
  hence thesis by Lm7,FUNCT_1:49;
end;
