cloche
could be a watch cap or a skullcap maybe even a slough hat
A toboggan hat is a ski cap. It is a close-fitting woolen cap and often has a tapering tail with a tassel. A toboggan isn't acknowledged as a hat by all sources; however, many dictionaries and Wikipedia do recognize it.
* rounded brimless cap fitting the crown of the head * the dome of the skull
"transmission fluid leaking from fitting below radiator cap after replacing radiator on 99 surburban
A coif is basically a kind of close-fitting cap, like a skullcap. The term can also be used for a kind of combination helmet/neck protector piece of armor.
Skullcap has two word definitions. The word 'skullcap' is defined as a small close-fitting cap without a brim on it. The word 'skullcap' also means the top part of the skull.
The traditional stocking cap worn by Danish men came in brown or red. The top of the cap was not close-fitting, it was longish and folded across the top of the head. Some of them had a tassel on the end.
Berets are soft, visorless cap with a close- fitting headband and a wide, round top upon often with a tap at it corner. Berets can also be a clip that you put in your hair to keep it from going every where.
A clergyman's cap is called a biretta.
The cervical cap
You don't need to shave your head before you wear a wig. Many wear a close-fitting cap to contain their hair under a wig. In any case, a wig will be warm.
The metal cap has a high expansion coefficient when temperature rises. As it expands and the grip loosens.