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.
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.