I define a "closed system" as one that is entirely self-sufficient, requiring no energy or other forms of input from outside the boundaries of the "system."

One of my colleagues has a glass globe on his desk, entirely sealed up, with a small plant and a couple of tiny fish in it.  From a nutrient perspective, this is a closed system since nothing in the way of nutrients can get in or out of the sphere.  However, sunlight can get and cause photosynthesis.  So I would call this a closed system, with the exception of energy being added via sunlight.

Does an ocean require anything to be transferred into and out of it in order to remain stable?  Does water ever leave the ocean through a natural means and enter some other system?  What about evaporation causing atmospheric moisture and then rain on the continents?  Does fresh water entering the oceans from rivers make oceans non-closed?

Compared to our oceans, a bathtub is a closed system.  If you bathe day after day in the same tub of water, that water will get dirtier and dirtier and the water level will drop due to evaporation and not be replenished.  Does this happen to the oceans?

So I think your task is to create a definition of "closed" for the oceans, something like "has no exchange of resources (water) with other planetary systems (like weather and rivers)" and then give examples where this is not true.