In geometry, a hyperplane is a subspace whose dimension is one less than that of its ambient space. If a space is 3-dimensional then its hyperplanes are the 2-dimensional planes, while if the space is 2-dimensional, its hyperplanes are the 1-dimensional lines. This notion can be used in any general space in which the concept of the dimension of a subspace is defined. The difference in dimension between a subspace S and its ambient space X is known as the codimension of S with respect to X. Therefore, a necessary condition for S to be a hyperplane in X is for S to have codimension one in X.
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