bandeau
A garment similar and related to the tube top, it is a narrow, band-shaped covering for the breasts. Its shape is used for swimsuit tops, undergarments and casual wear. In most cases, a bandeau is effectively a tube top that is narrow enough that it only covers the breasts and nothing more.
Some designs of the bandeau can make it easy for it to slip off the breasts, so a common addition is a halterneck to reduce the chance of slippage. Some designs are front-tie, while others may feature O-rings.