theorem Th24: :: TOPREAL4:24

for P, R being Subset of (TOP-REAL 2)
for p being Point of (TOP-REAL 2) st R is being_Region & P = { q where q is Point of (TOP-REAL 2) : ( q <> p & q in R & ( for P1 being Subset of (TOP-REAL 2) holds
( not P1 is_S-P_arc_joining p,q or not P1 c= R ) ) ) } holds
P is open