formula

$&&U_n'\stackrel{{\rm def}}{=}U_n\setminus \bigcup_{k=1}^n\bar{V}_k,\quad V_n'\stackrel{{\rm def}}{=}V_n\setminus \bigcup_{k=1}^n\bar{U}_k,\\ &&U\stackrel{{\rm def}}{=}\bigcup_{n=1}^{\infty}U_n',\quad V\stackrel{{\rm def}}{=}\bigcup_{n=1}^{\infty}V_n'$