Essential component of the BHC complex, a corepressor complex that represses transcription of neuron-specific genes in non-neuronal cells. The BHC complex is recruited at RE1/NRSE sites by REST and acts by deacetylating and demethylating specific sites on histones, thereby acting as a chromatin modifier. In the BHC complex, it serves as a molecular beacon for the recruitment of molecular machinery, including MeCP2 and SUV39H1, that imposes silencing across a chromosomal interval. Plays a central role in demethylation of Lys-4 of histone H3 by promoting demethylase activity of KDM1A on core histones and nucleosomal substrates. It also protects KDM1A from the proteasome. Component of a RCOR/GFI/KDM1A/HDAC complex that suppresses, via histone deacetylase (HDAC) recruitment, a number of genes implicated in multilineage blood cell development and controls hematopoietic differentiation. {ECO:0000269|PubMed:11171972, ECO:0000269|PubMed:11516394, ECO:0000269|PubMed:12032298, ECO:0000269|PubMed:12399542, ECO:0000269|PubMed:12493763, ECO:0000269|PubMed:16079794, ECO:0000269|PubMed:16140033}. This is the function of RCOR1 (REST corepressor 1, ENSG00000089902).