Perhaps cupboard would be considered. In Australia, we rarely talk about closets.
In the UK too. A closet is something you come out of if you are gay and are going public about it. You put your clothes (and your sheets) in a cupboard
Are you telling me that you don't even use the word closet to refer to a very small storage room? That's weird. I always took it for granted that cabinets and cupboards were boxes that hang on the wall, and closets were separate rooms.
As a US native English speaker I would only refer to a cabinet as something in the kitchen or bathroom. Otherwise I would use closet (if built in) or wardrobe (if furniture, like to Narnia). Does kast refer to each of those things?
As a non-native English speaker I would also only refer to a cabinet as something in the kitchen or bathroom. I do not understand why wardrobe is not accepted as a valid answer.
There are several mistakes in that link. Closets aren't necessarily small compared to wardrobes. In fact, a small bedroom can be referred to as a closet. The main difference is that a wardrobe is used specifically for clothes while closets are more general. A closet is usually a built-in side-room or recess, whereas a wardrobe tends to be a free-standing piece of furniture, although it can also be a room.
There seems to be a misunderstanding of seasonal wardrobes too. A summer wardrobe is the collection of clothes used in summer, rather than a piece of furniture that contains them. It's not unusual to keep your summer wardrobe and your winter wardrobe in the same piece of furniture, which is also called a wardrobe.
A wardrobe in the theatrical context is usually a room rather than a piece of furniture.
I know what you mean, but when we talk about wardrobes this is what comes to my mind: http://cdn.homedesignlover.com/wp-content/uploads/2013/05/15-oak-red-floral.jpg
It's sort of the kind of wardrobe I have :) If you can call that a wardrobe (now I'm not sure anymore :P )
Yeah, that's a wardrobe :)
It's also a closet. There's plenty of overlap.
What about "het laken is in de kast"? Would you ask "Waar is het laken" or "Waar ligt het laken"? This may be nonsense, but maybe "ligt" in this case means that the sheet is placed in the closet; that is it's usual place, it spends time in there... rather than it is just currently in there.
Imagine a cartoon where objects are alive, and the sheet hid in the closet. The bed asks the pillow where is the sheet, and the pillow says "het is in de kast"
Does any of this make sense?
Well... The scentences is gramatically right but other than that no. I think "ligt" here means the object is in something i.e "de lakens liggen in de kast" :)
What did I do wrong with "the sheet is in the chest" ? Doesn't anyone keep bed linen in a blanket chest any more?