theorem Th44: :: TSEP_1:44

for X being TopSpace
for A1, A2 being Subset of X holds
( A1,A2 are_separated iff ex C1, C2 being Subset of X st
( A1 c= C1 & A2 c= C2 & C1 misses A2 & C2 misses A1 & C1 is open & C2 is open ) )