While modern mathematics use many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. [1][details 1] A space consists of selected mathematical objects that are treated as points, and selected relationships between these points. The nature of the points can vary widely: for example, the points can be elements of a set, functions on another space, or subspaces of another space. It is

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... he relationships that define the nature of the space. More precisely, isomorphic spaces are considered identical, where an isomorphism between two spaces is a one-to-one correspondence between their points that preserves the relationships. For example, the relationships between the points of a three-dimensional Euclidean space are uniquely determined by Euclid's axioms, [details 2] and all threedimensional Euclidean spaces are considered identical.