The Space Between Things
Mathematical space is not a tightly defined concept. In fact, mathematical space is a series of loosely related concepts: Euclidean space, vector space and dimensional space being examples.
Physical space is a basic unit of reality. It can't be broken down further, thus it is defined by measurement. Five feet. Ten feet. One million feet.
Personal space is the place between things. It's my blank face. It's why I didn't get up this morning at seven to meet for coffee. Space can't be broken down further.