Are Manchester United based in city of Manchester?

There is a CITY of Manchester, and also the ADMINISTERY AREA of Greater Manchester, which includes such towns as Stockport and Oldham. This, along with Merseyside, another Administery Area, with Liverpool as its main city, were carved out of Lancashire as having common needs, being mainly urban, different to the rest of Lancashire, which is mainy rural. For this reason it is debatable as to wether Greater Manchester, supposably still part of the County of Lancashire, can be classed as a county, although most people do.