Any headwear that atypically leaves the crown of the head exposed, either by design or due to damage.
Note that this excludes headwear that already has applicable terminology on Danbooru - such as visor caps being the 'open' variant of baseball caps.
One example of an open hat is the traditional Chinese "Cooling hat"/"Hakka hat" (Liangmao). This bears resemblance to ajirogasa, with the exception of a circular cutout in its middle. This modification is applied to keep the wearer's head cool in hot weather.
