Space concepts are different in Mathematics and Physics, even though Physics has to use the mathematical space concept abstractly when it uses math.  However, in real modern physical world there is no pure, fixed, independent and empty space even we feel it is there in our everyday life .   TD Lee considered  empty  is the most basic status of  matter.  He said he got the idea from Chinese culture.   K19 may be interested in that.  :-).

It is hard to distinguish these two kinds of space concepts. In other words, we have to understand what is the physical essentials under its mathematical expression.