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. Together with RMI1, is essential for the resolution of meiotic recombination intermediates, a step that prevents entanglement of the parental chromosomes. May have DNA decatenation activity. 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. The RMI complex interacts with RECQL4A (By similarity). Severe developmental defects and early lethality. Belongs to the type IA topoisomerase family.