Generalizations of a theorem of doležal

N. Bourbaki,Algebra, Chap. 7, 2nd Edition, Hermann, Paris, 1964. V. Doležal, The existence of a continuous basis of a certain linear subspace ofE r which depends on a parameter,Cas. Pro. Pest. Mat. 89 (1964), 466–468. T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966, pp. 121–122. F. Rellich, Storungstheorie der Spektralzerlegung, I,Math. Ann. 113 (1931), 600–619. Leonard Weiss andP. L. Falb, Doležal's theorem, linear algebra with continuously parametrized elements and time-varying systems,Math. Systems Theory 3 (1969), 67–75.