confirming the predictions of Einstein's theories, and non-Euclidean geometry is usually used to describe spacetime. Mathematics In modern mathematics spaces are defined as sets with some added structure. They are frequently described as different types of manifolds, which are spaces that locally approximate to Euclidean space, and where the properties are defined largely on local connectedness of points that lie on the manifold. There are however, many diverse mathematical objects that are called spaces. For example, vector spaces such as function spaces may have infinite numbers of independent dimensions and a notion of distance very different from Euclidean space, and topological spaces replace the concept of distance with a more abstract idea of nearness. Physics Space is one of the few fundamental quantities in physics, meaning that it cannot be defined via other quantities because nothing more fundamental is known at the present. On the other hand, it can be related to other fundamental quantities. Thus, similar to other fundamental quantities (like time and mass), space can be explored via measurement and experiment. Today, our three-dimensional space is viewed as embedded in a four-dimensional spacetime, called Minkowski space (see special relativity). The idea behind spacetime is that time is hyperbolic-orthogonal to each of the three spatial dimensions. Relativity Before Albert Einstein's work on relativistic physics, time and space were viewed as independent dimensions. Einstein's discoveries showed that due to relativity of motion our space and time can be mathematically combined into one object–spacetime. It turns out that distances in space or in time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space along spacetime intervals are—which justifies the name. In addition, time and space dimensions should not be viewed as exactly equivalent in Minkowski space. One can freely move in space but not in time. Thus, time and space coordinates are treated differently both in special relativity (where time is sometimes considered an imaginary coordinate) and in general relativity (where different signs are assigned to time and space components of spacetime metric). Furthermore, in Einstein's general theory of relativity, it is postulated that spacetime is geometrically distorted – curved – near to gravitationally significant masses. One consequence of this postulate, which follows from the equations of general relativity, is the prediction of moving ripples of spacetime, called gravitational waves. While indirect evidence for these waves has been found (in the motions of the Hulse–Taylor