In order to ellucidate these points, I need to explain the meaning of some of the concepts involved.
The primary meaning of `space' is that of the flat, Euclidean, 3-dimensional space of our everyday actions. Mathematicians have then got hold of this idea and made use of it for their own purposes, generalising the meaning in a number of different ways, altering or weakening some aspects of the basic Euclidean idea.
The simplest generalisation is to many-dimensional space. This involves keeping the same geometric properties (except where these refer explicitly to the number of dimensions) and in particular the same concept of symmetries: the principle that all directions in the space are absolutely equivalent. The only thing that is altered is the number of mutually perpendicular lines that can be drawn through any given point, which is increased from 3 to some greater number n. Mathematicians refer to this as n-dimensional Euclidean space; not thereby claiming that Euclid would recognise it, but signaling that little has been altered from the Euclidean picture, beyond the dimension. Saying that mind is located in such a space is to assert something very specific about the existance of a higher dimensional geometry that mimics Euclidean geometry. There has never been any evidence for such a geometry, and there are practically no physical theories that postulate it. The many higher dimensional physical theories that are in vogue all involve spaces that are not Euclidean.
There is a different sort of generalisation, known as curved space (in which I include curved space-time). This involves altering the basic geometry of the space: it is supposed to be of an approximately Euclidean form over very small regions, but over large regions all geometrical properties (rules about the existence of lines, planes and so on) break down. One can combine curvature with increased dimensions. The simplest higher-dimensional physical theories are of this form. We would only be entitled to assert that mind occupied a space such as this if we had evidence of a small-scale Euclidean structure and of its non-Euclidean breakdown on larger scales.
There are a number of other more extreme generalisations that drop the Euclidean structure even at small length scales. These include metric spaces, where there exists a concept of distance, as well as topological and fuzzy spaces where there is only a concept of nearness. To make matters more confusing, metric spaces carry with them a definition of dimension which is different from the geometrical sense of dimension examined earlier.
One might well ask, since these generalisations are so very different from the space of our awareness, is it not confusing to call them `spaces' at all? The mathematician might defend the name by saying that all these generalisations involve their own particular sorts of laws which generalise the laws of geometry that hold in ordinary space, and thereby entitle one to call the result a space. Without such quasi-geometrical laws one would have not a space but a set. A marginal position, between set and space, is occupied by fuzzy set theory (which I shall refer to later) where the word ``space'' is occasionally used.
All these generalisations are useful both in physics and psychology. Curved space-time is used to study gravity, tolerance geometry has been used to study the colour space that encodes our visual perception of extended areas of colour (Zeeman, 1962). It will probably turn out that all these concepts are needed for different aspects of mind. Yet mind itself, I want to argue, is not located in any of them.