A note on basic sets of homogeneous harmonic polynomials
E. P. Miles, Ernest Williams · Proceedings of the American Mathematical Society · 1955
BASIC SETS OF HOMOGENEOUS HARMONIC POLYNOMIALS 769 and in G must separate G.But by Theorem I this set is 0-dimensional, a contradiction.Hence some element of G intersects each of 7>i and D% and thus some element of G' contains an arc h with endpoints in 7>i and D2 respectively.But by an argument similar to that used in the proof of Theorem I we can exhibit an open subcollection U of G with U containing g and with U-U countable, a contradiction.