reserve A, B, X, Y for set;
reserve R, S, T for non empty TopSpace;

theorem Th34:
  for J being Basis of T holds J is non empty
proof
  let J be Basis of T;
  assume J is empty;
  then
A1: UniCl J = {{}} by YELLOW_9:16;
  the topology of T c= UniCl J & the carrier of T in the topology of T by
CANTOR_1:def 2,PRE_TOPC:def 1;
  hence contradiction by A1,TARSKI:def 1;
end;
