Releases the supercoiling and torsional tension of DNA introduced during the DNA replication and transcription by transiently cleaving and rejoining one strand of the DNA duplex. Introduces a single-strand break via transesterification at a target site in duplex DNA. The scissile phosphodiester is attacked by the catalytic tyrosine of the enzyme, resulting in the formation of a DNA-(5'-phosphotyrosyl)-enzyme intermediate and the expulsion of a 3'-OH DNA strand. The free DNA strand then undergoes passage around the unbroken strand thus removing DNA supercoils. Finally, in the religation step, the DNA 3'-OH attacks the covalent intermediate to expel the active-site tyrosine and restore the DNA phosphodiester backbone. Essential component of the RMI complex, a complex that plays an important role in the resolution step of homologous recombination, in a process called Holliday Junction dissolution, to limit DNA crossover formation in cells (By similarity). ATP-independent breakage of single-stranded DNA, followed by passage and rejoining. Binds two Mg(2+) ions per subunit. Component of the RMI complex, containing at least TOP3A and RMI1. Belongs to the type IA topoisomerase family.