for A being Subset of (TOP-REAL 2) st A ` <> {} holds
( ( A is boundary & A is Jordan ) iff ex A1, A2 being Subset of (TOP-REAL 2) st
( A ` = A1 \/ A2 & A1 misses A2 & (Cl A1) \ A1 = (Cl A2) \ A2 & A = (Cl A1) \ A1 & ( for C1, C2 being Subset of ((TOP-REAL 2) | (A `)) st C1 = A1 & C2 = A2 holds
( C1 is a_component & C2 is a_component ) ) ) )