Description
An arbitrary collection of homogeneous objects (events, states, functions, figures, values of variables, etc.) between which there are relationships similar to the usual spatial relations (continuity, distance, etc). In regarding such a collection of objects as a space, all properties of these objects except those that are determined by these spacelike relationships are ignored. The relations then determine the structure or geometry of such a space. Spaces can be classified with respect to the types of those spacelike relations that underlie their definition. For example: a metric space is a set of arbitrary elements (points) between which a distance is defined; a topological space is any collection of points, in which a relation of neighbourhood of one point to a set of points is defined and, consequently, a relation of neighbourhood or adherence of two sets (figures) to one another.
When the position of a point cannot be defined by three coordinates, the concept of a many-dimensional space is introduced. If some figure or the state of some system, etc., is given by n data, then this figure, state, etc., can be conceived as a point of some n-dimensional space. This permits the application of well-known geometric analogies and methods to the study of the phenomena in question.