Lac operator is a
Operators are DNA cis-acting regulatory sequences located contiguous to genes they control on same chromosome, functioning regardless of homologous DNA elsewhere. lacO consists of 21 base pair symmetric site with inverted repeat matching LacI recognition helices, overlapping transcription start. Mutated operator affects only downstream lacZYA genes on same DNA strand, demonstrating cis dominance typical of promoters and operators. Trans-acting diffusible proteins like LacI or CAP can complement and act on both chromosomes in partial diploids, unlike cis elements. Enzyme coding regions are down
Ref: Alberts Chapter 7 Definitions - operator cis-acting sequence; NCBI Genetics - cis regulatory elements act on same DNA molecule