An enzyme that creates or changes the state of a topoisomer, particularly a topoisomer of DNA. Such enzymes change the way in which DNA is packaged in living cells by altering the degree of supercoiling of the DNA molecules. For example, DNA gyrase, a topoisomerase found in E. coli, introduces negative supercoiling by breaking both strands of the DNA double helix and passing another stretch of the double helix through the gap, which is then sealed. This creates a twist in the circular DNA of the bacterial chromosome. Other topoisomerases can remove supercoiling by introducing a temporary break in one DNA strand and passing the other strand through it.