theorem Th38: :: TOPALG_6:38

for T being non empty TopSpace
for c1, c2 being with_endpoints Curve of T st sup (dom c1) = inf (dom c2) & the_last_point_of c1 = the_first_point_of c2 holds
( c1 + c2 is with_endpoints & dom (c1 + c2) = [.(inf (dom c1)),(sup (dom c2)).] & (c1 + c2) . (inf (dom c1)) = the_first_point_of c1 & (c1 + c2) . (sup (dom c2)) = the_last_point_of c2 )