ABSTRACT
The number of dimensions of a continuous space is, like continuity itself, a "topological invariant" of that space. We can define the dimension-number of a space as the number of coordinates needed to specify completely, but no more than completely, the "position" of a point. We shall consider how many questions any scheme for labelling points of a space must ask in respect of any point if it is to label it adequately and economically. It has been shown that the number of questions is independent of the particular labelling scheme adopted, and depends only on the space. We can also keep continuity provided we accept some degree of inadequacy or redundancy. Obviously we can redescribe part of a two-dimensional space in a one-dimensional way, preserving continuity, for we can do that much with any line in the plane.
