If the spoon was one of those spoons with holes in the, non-handle-part, then I think it would have to produce a discontinuity.
But for a normal spoon shape, I don’t think dipping it in makes the map between points in the water fail to be continuous.
I’m somewhat confident that there is a smooth path from an embedding of a cylinder to R^3 to an embedding of a cylinder which is a little taller and has a spoon shape removed from it, into R^3 .
But for a normal spoon shape, I don’t think dipping it in makes the map between points in the water fail to be continuous. I’m somewhat confident that there is a smooth path from an embedding of a cylinder to R^3 to an embedding of a cylinder which is a little taller and has a spoon shape removed from it, into R^3 .