Here to enumerate a few. In physics only the 3rd dimension makes sense where experimentation has shown that any dimension other than 3rd leads to the wrong physics of Newtonian Classical. That alone should have alerted the math community that there definition of higher dimensions were pure illusions, Loch Ness monsters. Math people once they hear this idea they sheepishly accept it as clear as broad daylight. But we should require a proof of this.
Point deletions are always possible, but point compactification is silly.
The idea that the Euclidean plane can be infinite in reach is not a true idea. One must prove it first if it is true. I believe it is false by the following argument on Reals or the Complex plane. The infinite Euclidean Plane is a contradiction in terms. The Euclidean Plane to exist must exist as a finite plane.