Taking your dog for a walk by bicycle is quite a common sight in Japan.
Small breeds of dog are also much more popular than larger dogs here, due to the very small, or non-existent yards in many residential properties. It is much easier to keep small dogs indoors.
It is also much more common to see women with small dogs than men, who seem to be the walkers of the few larger breeds that you do see here.
The basket on the front of the bicycle is to put the dog in when it gets tired, or when in heavy car traffic.
