theorem Th2: :: TOPREAL1:2

for T being T_2 TopSpace
for P, Q being Subset of T
for p1, p2, q1 being Point of T st P is_an_arc_of p1,p2 & Q is_an_arc_of p2,q1 & P /\ Q = {p2} holds
P \/ Q is_an_arc_of p1,q1 by TOPMETR2:3;