Headwear that includes an opening at the top. Might be called a "half-hat" or a "topless hat".
This can include traditional Chinese "Cooling hats"/"Hakka hats" (Liangmao), which have a cut in the middle to keep the wearer's head cool.
Do not use for visor caps. Do not use when hair through headwear or ears through headwear would suffice; the hat's design must be significantly altered.