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I am troubled by the conventional image of space being inverted by a black hole - if that's the correct way to phrase it. But I'd like to take a step back and use a model to explain.

We observe an enclosed room, shaped like a cube, with 1,000 cubic feet of space (10x10x10).

Then in this room we place, in the center of the floor, a cube shaped sponge, which is 125 cubic feet (5x5x5).

So the space in the room is now less than 1,000 cubic feet. It would be 1,000 minus 125 = 875. Yet, we still have to account for the space within the cube shaped sponge. For the sake of discussion, the cube shaped sponge here has 25 cubic feet of space within it. So add 25 to 875, and the space in the room is now 900 square feet. The matter takes up 100 cubic feet within the cube shaped sponge.

Now we add matter to the sponge until it's infinitely dense. There is now no more space with the sponge. That means the space within the room drops to 875 cubic feet, and the infinitely dense matter within the cube space sponge takes up 125 cubic feet.

Thus, having no space within the sponge - the question is "would this now be considered a hole in space?" A hole in space must take up 3-dimensional space. It's seems counter-intuitive to how a layman would describe a hole. A conventional hole is a hole in matter, which would increase space. But a hole in space would to the contrary, increase matter and decrease space.

Is this correct? The initial aspect of the infinitely dense matter would be a "hole in space." Is this different than a "black hole in space," where I envisioned the inversion of space due to space being unable to manage the effects of infinite density in its normal state (as we normally see it)? Or is a black whole still using up space (as described above) to the extent of its dimensions as an object of matter?

Thanks, Dave