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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.

user3520363
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    I'm sorry, I don't know if it's a language barrier or simply fuzzy thinking, but as written this question is absolutely incomprehensible and impossible to answer. – Jack M Jul 08 '18 at 22:03
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    Yes, we can think of such a thing. Does this answer your question? – uniquesolution Jul 08 '18 at 22:18
  • On the Physics side presumably you are talking about one particular currently known mathematical model of physical space (of which there are many inconsistent/incompatible ones to choose from) rather than talking about the one observed reality itself. – James Arathoon Jul 08 '18 at 22:43
  • How you understand if you works in a physical space or, instead, in a mathematical space? You need a measure or something to understand or discriminate each other, right? What is the name of this 'measure'? (A measure is an additive function if I remember well) – user3520363 Jul 09 '18 at 10:30
  • If you bring all the evidence together physical space cannot be represented by a single perfectly linear mathematical model. If we limit ourselves to certain well defined and limited physical domains of application then linear mathematical approximations, where the assumption of superposition holds, can be found to work surprisingly well - so surprisingly well it often defies belief. Ultimately though the physical space we observe is non-linear in some strange way no one yet understands; as to move further now we must add gravitational forces to our atomic and sub-atomic models somehow. – James Arathoon Jul 09 '18 at 14:43
  • @JamesArathoon - this is a good answer, so the key to 'enter' in a mathematical space from a physical space can be visualized like a well defined and limited physical domains of application ? Remember dimension or some measurement type definition your analogy. How is called this operation in mathamatics ? It is enough for me to grasp the intuition, but I think it better if you help me using mathematical term or if you provide me an example. – user3520363 Jul 09 '18 at 18:43
  • From physical observation to simplified/idealised mathematical model the precise details of non-linearities and many other extraneous details not considered relevant at the time are lost. This process is studied by scientists and philosophers not generally mathematicians. On the mathematical side the information and context used to physically propose the mathematical model has all been lost. It would be very inefficient indeed just to study mathematics if your ultimate aim was to propose new mathematical models for physics. Its like a one way mathematical function. – James Arathoon Jul 09 '18 at 19:13
  • @JamesArathoon in mathematical terms, what does this model remind you of ? physical-math space model – user3520363 Jul 09 '18 at 19:42

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