for p being Point of (TOP-REAL 2)
for P, R being Subset of (TOP-REAL 2) st R is being_Region & p in R & P = { q where q is Point of (TOP-REAL 2) : ( q = p or ex P1 being Subset of (TOP-REAL 2) st
( P1 is_S-P_arc_joining p,q & P1 c= R ) ) } holds
P is open