In the scope of spatial relations, the word "on" in English typically describes the state where one object is positioned directly above another object, where the lower object supports the upper one. For example, "the bottle is on the table".
However, in the same scope of spatial relations, it has another meaning which is not only related to up/down. For example, "the picture is on the wall" describes a similar concept, that does not apply just to the up/down axis.
Is there any antonym for "on" that would capture both cases?
EDIT: To be clear, I'm looking to the antonym in the sense that it's the opposite role. For example, if the "ceiling is above the floor", then the "floor is below the ceiling" and "below" is the antonym of "above".
As the wall is "supporting" the picture (when the picture is on the wall) and the table is "supporting" the bottle (when the bottle is on the table), the question if there's a better word than "support"?