A physical space use a physical lenght, they talk about 'base unit' or magnitude like a 'quantity' of a object but at the end physics and mathematics meet together and speak the same language in a common place: dimension.
So here we can discriminate and jump from physical definition to mathematical definition: now we are in an euclidean space $\rightarrow$ euclidean metric.
So.. between physical space definition and mathematical space definition we have a topological space: it's like a window.
Can we think of such a thing?
P.S: I had also thought of a quotient space but the definition of topological space seems to me the most general.