J. Arthur Rank but continued to handle all distribution for the Rank organisation until 1955, when it was renamed J. Arthur Rank Film Distributors. In 1939 Rank consolidated his film production interests in both the Pinewood Film Studios and the Denham Film Studios. In 1938 Rank bought the Odeon Cinemas chain. and the Amalgamated Studios in Elstree, although the latter were never used as film studios by Rank. In 1941, it absorbed the Gaumont British, which owned 251 cinemas, and the Lime Grove Studios, (later owned by the BBC) and bought the Paramount Cinemas chain, so that by 1942 the Rank Organisation owned
Tensor rank decomposition formula_23 form a dense set formula_28: every tensor in the aforementioned space is either of rank less than the generic rank, or it is the limit in the Euclidean topology of a sequence of tensors from formula_28. In the case of real tensors, the set of tensors of rank at most formula_23 only forms an open set of positive measure in the Euclidean topology. There may exist Euclidean-open sets of tensors of rank strictly higher than the generic rank. All ranks appearing on open sets in the Euclidean topology are called typical ranks. The smallest typical rank is called the