The Practice Effect, a 1984 novel by David Brin, also the answer to this old question. Any of these covers ring a bell?
A scientist by the name of Dennis Nuel is working at, and attending, an institute of scientific research and pioneering work into the fictional scientific field of "Zievatronics", the manipulation of Time and Space. After the death of his mentor, however, he is taken off the project and another professor takes over.
After a time, the device that has been created to move through space and time, known as the "Zievatron" encounters operational problems and is fixed to the co-ordinates of a world that appears to be very similar to our Earth in most respects, and Dennis is re-recruited to help fix it. He volunteers to be sent to the other world in order to fix the other part of the Zievatron. On arriving to this planet, he finds the Zievatron dismantled and critical parts of it missing. Of the three surveillance robots sent through to this planet, he finds two have also been broken apart. After a while, he finds the last robot, intact and still functioning, and uses it to view any recorded images that might help him identify what it was that happened to the Zievatron.
In this world, instead of objects wearing out as you use them, they improve. This is referred to as the Practice effect. For example, swords get sharper with use, baskets get stronger the more things they carry, mirrors, furniture and decorations look more attractive the more they are looked at. The downside to this being that an object's condition deteriorates over time if not put to use. Under this system, members of society's higher strata employ servants to Practice their own possessions to perfection.
It is eventually discovered that the Practice Effect is the result of an elusive, biologically-engineered creature known as a Krenegee Beast that causes a change in a law of thermodynamics. This creature emits a field under which the Practice Effect works. The closer one is to the Krenegee Beasts, the more efficient the Practice that is done. The Practice Effect can take many months before an object reaches its maximum point of "practice", but the process is sped up if one is under a Felthesh Trance. The presence of a Krenegee Beast speeds up the process more than a Felthesh Trance.
An excerpt about the zipper-saw:
The zizzing sound behind them suddenly ended in a sharp snap. Young Gath held up the severed end of the piece of wood, beaming at Dennis admiringly.
"The flexible saw worked!" he whispered in excitement. He looked around to make sure no guards were near, then handed the tool to Dennis.
The teeth were warm from friction. On Earth they would have shown signs of wear after cutting just that little piece of soft wood. But Gath had been thinking "Cut! Cut!" as he worked. And now, thanks to the gentle practice, the zipper was just a little sharper than before.
Dennis shook his head. It was a helluva purpose to put a zipper to. Those sealing the pockets of his overalls were all of soft plastic. He had had to rip the metal zipper from his pants—his fly was now shut with three crude buttons that he hoped would get better with use. Certainly he wasn't about to use this zipper in its old purpose again!
"Good work, Gath. We'll arrange for you to get on sick call so you can practice this one to perfection. The night it's finished—"
Arth interrupted quickly with a comment on the weather. In a moment a pair of guards passed nearby. The prisoners developed an interest in their meal until they had gone.