theorem Th11: :: TOPDIM_2:11

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