Mary Hogarth beautiful and light-hearted". When Robert Story visited the Hogarth household in 1836, he described Hogarth as "the fairest flower of spring". Dickens showed particular affection to Hogarth, and described her as "a close friend, an exceptional sister, a companion at home." It is believed that Hogarth was the first person to read "The Pickwick Papers" and "Oliver Twist", as Dickens valued Hogarth's input and feedback more than his wife's. In the early hours of 7 May 1837, after Hogarth had returned from a showing of "Is She His Wife?" at the St James's Theatre with the Dickens couple, she collapsed
Arrangement of hyperplanes convenient to allow the degenerate hyperplane, which is the whole space "S", to belong to an arrangement. If "A" contains the degenerate hyperplane, then it has no regions because the complement is empty. However, it still has flats, an intersection semilattice, and faces. The preceding discussion assumes the degenerate hyperplane is not in the arrangement. Sometimes one wants to allow repeated hyperplanes in the arrangement. We did not consider this possibility in the preceding discussion, but it makes no material difference. Arrangement of hyperplanes In geometry and combinatorics, an arrangement of hyperplanes is an arrangement of a finite set "A"