theorem :: TOPDIM_2:12

for n being Nat
for TM being metrizable TopSpace st TM is finite-ind & TM is second-countable & ind TM <= n holds
for A, B being Subset of TM st A is closed & B is closed & A misses B holds
ex L being Subset of TM st
( L separates A,B & ind L <= n - 1 )