Histone demethylase that specifically demethylates Lys-9 and Lys-36 residues of histone H3, thereby playing a central role in histone code (PubMed:26741168). Does not demethylate histone H3 Lys-4, H3 Lys-27 nor H4 Lys-20. Demethylates trimethylated H3 Lys-9 and H3 Lys-36 residue, while it has no activity on mono- and dimethylated residues. Demethylation of Lys residue generates formaldehyde and succinate. Participates in transcriptional repression of ASCL2 and E2F-responsive promoters via the recruitment of histone deacetylases and NCOR1, respectively.