theorem Th29:
for
S,
T being non
empty TopSpace for
f being
continuous Function of
S,
T for
a,
b,
c being
Point of
S for
P being
Path of
a,
b for
Q being
Path of
b,
c for
P1 being
Path of
f . a,
f . b for
Q1 being
Path of
f . b,
f . c st
a,
b are_connected &
b,
c are_connected &
P1 = f * P &
Q1 = f * Q holds
P1 + Q1 = f * (P + Q)