top piece noun3 •(US, informal) Something worn on the head; a hat, a wig or toupee.The Mayor took himself up in the lift, quite naked of course, except for his top-piece and neckpiece with his two shopping-bags […]. — 1973 •The part of the heel on a shoe or boot that comes into contact with the ground.Then pare the top piece to the size and form you intend it to be; but that you should always do before the heel is sewed, for now you are confined to the channel. — 1834 •The head or brain. formstop pieces