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The difference in dimension between a subspace S and its ambient space X is known as the codimension of S with. While a hyperplane of an n-dimensional projective space does not have this property. Fano, Sulle varietà algebriche a tre dimensioni le cui sezioni iperpiane sono superficie di genere zero e bigenere uno, Memorie società dei XL, 24 (1938), pp. For instance, a hyperplane of an n-dimensional affine space is a flat subset with dimension n 1 and it separates the space into two half spaces.
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