Holes are made of space by definition, therefore spacetime is a hole.
Definitely not true in math - if you take a circle (S^1 = { (x, y) : x^2 + y^2 == 1 }) it has a hole as defined by homotopy in the middle and there is no 'space' there. If you fill it with space you get a disk (D^2 = { (x, y) : x^2 + y^2 <= 1 }) there is no longer a hole as defined by homotopy/is contractible.
The one that defines the noun, "hole," as a hollow place in a solid body or surface.
> if you take a circle (S^1 = { (x, y) : x^2 + y^2 == 1 })
Black holes are real, but your circle can only "exist" in mathematics.
You are aware that General Relativity is about the most mathematical (and mathematically rigorous and mathematically advanced) theory we have in physics? Several predictions were made purely based upon mathematical arguments, without much physical input. So your argument that math were a "different realm" with no connection to reality is full of, uhh, holes.
In fact, I would argue mathematics is mainly a language that provides us with the precision that everyday language lacks, it's a tool that allows us to make precise arguments while ruling out logical fallacies.
In the present case it allows us to say very precisely what we mean by a hole. This definition[0] has been employed in countless predictions in physics and its usefulness has been confirmed by experiment. Meanwhile, your definition is vague at best.
[0]: Look up "simple-connectedness" or, more generally, "homotopy groups".
This straw man was not my argument. My argument is that circles only exist mathematically.
But it doesn't matter. The definition of a hole doesn't rest on the definition of a circle.
No I don't, and this is still a straw man.
1) If a hole is made of space, it doesn't follow that space is a hole.
2) Space is not spacetime.
Yes, it absolutely does, so long as there is no category error, and there is none here. The Universe is just an inconceivably large, curved hole with a tiny little bit of stuff in it.
> 2) Space is not spacetime.
Einstein and I disagree with you. Prior to Einstein's work, space and time were independent dimensions. But over 100 years ago Einstein showed that relativity of motion mathematically combines space and time into one, spacetime. For all intents and purposes, anyone talking about space today under any circumstances is also talking about spacetime whether time is specifically mentioned or not it is always there along with space.