Primairly according to Kant space is a priory form that 'causes' that we can experience things in 3d. He argues this as follow:
"In the transcendental exposition, Kant refers back to his metaphysical exposition in order to show that the sciences would be impossible if space and time were not kinds of pure a priori intuitions. He asks the reader to take the proposition, "two straight lines can neither contain any space nor, consequently, form a figure", and then to try to derive this proposition from the concepts of a straight line and the number two.
He concludes that it is simply impossible. Thus, since this information cannot be obtained from analytic reasoning, it must be obtained through synthetic reasoning, i.e., a synthesis of concepts (in this case two and straightness) with the pure (a priori) intuition of space.
In this case, however, it was not experience that furnished the third term; otherwise, the necessary and universal character of geometry would be lost. Only space, which is a pure a priori form of intuition, can make this synthetic judgment, thus it must then be a priori. If geometry does not serve this pure a priori intuition, it is empirical, and would be an experimental science, but geometry does not proceed by measurements—it proceeds by demonstrations."
But is it excluded that space can be experienced or that it could be something in itself or a noumenon? Perhaps Kant himself doesn't say anything about this but could it be derived from his theory that it is possible or at least open?
Fe if you walk you experience distance and things has an extension what you can see, so why should it be a form a priori?