My gym states that they no longer use chlorine in their swimming pool. They state that they have installed a filter system that uses salt instead of chlorine because it is cheaper. I have never heard of this. Have you? Have you heard of using hydrogen peroxide instead of chlorine?
Yes - both of these (salt and hydrogen peroxide) are used in swimming pools. The likely misunderstanding is that the gym is no longer feeding chlorine in to the swimming pool. The fact is that a "salt" pool is generating chlorine by changing the salt in the swimming pool to chlorine and then back to salt. Hydrogen peroxide is a common "shock" chemical for non-chlorine systems such as biguanide.