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 than 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 (By similarity). Essential for proper chromosome segregation in both meiosis and mitosis. Weakly relaxes negative supercoils and displays a distinct preference for binding single-stranded DNA. The TOP3-SGS1 protein complex may function as a eukaryotic reverse gyrase introducing positive supercoils into extrachromosomal ribosomal DNA rings. ATP-independent breakage of single-stranded DNA, followed by passage and rejoining. Forms a complex with SGS1 and RMI1. Interacts with SGS1. Present with 468 molecules/cell in log phase SD medium. Belongs to the type IA topoisomerase family.