one thing to say "not safe" but how about "why?"
So here goes:
Batteries are a container for the chemicals and such inside of it that holds the electrical power. They are build similar to a cylinder type bottle (think of it like a thermos).
The insides are done is layers upon layers, which the content that is touching the walls is trying to pull in the electrons so the whole "thermos" is negative (so most of the body of the battery is negative).
The center is trying to push out the elections and is connected to the "lid" on top, which is the only part that is positive.
To prevent these two from touching, there is an insulator, which on these batteries is very thin, and if you would look at the top of a "naked" battery, you'd see that it's barely 1mm, yet enough to block the flow of power. But if anything makes a contact between this insulator, you have a short and the battery will fry, either vent, where enough power to "bake" the chemicals and the liquid shots out from the safety holes by the positive pin on top, or the short will cause a serious overload, making the chemical reaction to "runaway" and well.. boom!
To protect this small insulation, manufacturers have added an additional ring on top. This ring is held in place by the plastic heat-shrink wrap.
So if you damage the wrap, you are making it possible for this ring to fall off or have something slide under this ring, etc. and make this dangerous contact.
So it's a degree of safety, should the wrap be damaged on the lower end or the side, it's still not good, but a piece of tape is an okay temporary solution.
BUT, as your picture shows, the rip is at the top, in the worst area as you could rip it more, pop the ring off, etc. and have a short.
So as others stated, get it re-wrapped as soon as possible and in the meanwhile, place it in something that will prevent any sort of possible further damage or any contact.
