Why does "on top of" lack of an article before "top"? [closed]

I read in a children's book, Bliff’s fun phonics:

"The duck is on top."

"Top" is supposed to be countable. Why is there not an article before "top" in the phrase?

Solution 1:

The players:

• top is a noun that means "the highest point"
• on is a preposition meaning "to be in physical contact with"
• "The duck..." is the subject of this sentence.
• "...is on top." is the predicate of this sentence.

"Top" is supposed to be countable.

Not really. "Top" is just "top" and most things only have 1 top, tautologically speaking (there can only be 1 highest point). There is a separate noun, a top, like a spinning top, such as a dreidel, which could be countable. You could have 3 tops, so to speak, of that kind. You cannot have 3 tops to 1 duck.

"On top" is an established prepositional phrase, such as "by the way" or "in side", the former having become a hackneyed idiom and the latter going so far as to become 1 word.

There is no need to add an article if the context is sufficient to determine what the duck is on top of.

If you were being very expressive, here is an example scenario where a definite article might appear:

Where is the duck?

The duck is on the house.

Yes, but, where on the house is the duck?

On the top.

I don't think you would see this expression with an indefinite article outside of farfetched or idiosyncratic instances.

Note another interesting example:

"We put the flag on the top of the mountain."

"We put the flag on top of the mountain."

The first sentence implies that the speaker summitted the mountain and placed the flag at the (very) top. The second sentence could mean the same thing, to a lazy speaker and a lazy listener; it could also be a joke that the speaker put the flag "somewhere on top of the geographical feature of the mountain, but not necessarily the top."