The "normal sets" are separable metric spaces with no isolated points, as introduced by Fréchet in <A HREF="http://dx.doi.org/10.1007/BF03018603">*Sur quelques points du calcul fonctionnel*</A>, Rendiconti del Circolo Matematico di Palermo **22**, 1-74 (1906).

For an extensive discussion of Brouwer's paper in the historical context see D.M. Johnson's 1981 article in the <A HREF="http://dx.doi.org/10.1007/BF02116242">Archive for History of Exact Sciences</A>.