The term 'flat brimless hat' is often referred to as a CAP. A CAP is a type of headwear that is typically made of fabric or leather and has a visor or brim in the front. It is usually worn to protect the head from the sun or rain, or to keep the hair out of the face. The flat brimless hat is a variation of the traditional CAP, which has a brim that is either curved or flat. This type of hat does not have a brim, making it more lightweight and comfortable to wear. It is often used for casual occasions, such as sports or outdoor activities.