for TM being metrizable TopSpace
for M being Subset of TM
for A1, A2 being closed Subset of TM
for V1, V2 being open Subset of TM st A1 c= V1 & A2 c= V2 & Cl V1 misses Cl V2 holds
for mV1, mV2, mL being Subset of (TM | M) st mV1 = M /\ (Cl V1) & mV2 = M /\ (Cl V2) & mL separates mV1,mV2 holds
ex L being Subset of TM st
( L separates A1,A2 & M /\ L c= mL )