Histone demethylase that demethylates 'Lys-4' and 'Lys-36' of histone H3, thereby playing a central role in histone code (PubMed:16362057, PubMed:17994099, PubMed:26237645). Preferentially demethylates trimethylated H3 'Lys-4' and dimethylated H3 'Lys-36' residue while it has weak or no activity for mono- and tri-methylated H3 'Lys-36' (PubMed:16362057, PubMed:17994099, PubMed:26237645). Preferentially binds the transcribed region of ribosomal RNA and represses the transcription of ribosomal RNA genes which inhibits cell growth and proliferation (PubMed:16362057, PubMed:17994099). May also serve as a substrate-recognition component of the SCF (SKP1-CUL1-F-box protein)-type E3 ubiquitin ligase complex (Probable). {ECO:0000269|PubMed:16362057, ECO:0000269|PubMed:17994099, ECO:0000269|PubMed:26237645, ECO:0000305}. This is the function of ENSG00000089094 (KDM2B, lysine demethylase 2B).