Hermit crab wood and stone are used by some species). The tip of the hermit crab's abdomen is adapted to clasp strongly onto the columella of the snail shell. Most hermit crabs are nocturnal. Hermit crabs can be divided into two groups: As hermit crabs grow, they require larger shells. Since suitable intact gastropod shells are sometimes a limited resource, vigorous competition often occurs among hermit crabs for shells. The availability of empty shells at any given place depends on the relative abundance of gastropods and hermit crabs, matched for size. An equally important issue is the population of organisms that prey
History of manifolds and varieties spaces with a differentiable or topological structure, while "variety" refers to spaces with an algebraic structure, as in algebraic varieties. In Romance languages, manifold is translated as "variety" – such spaces with a differentiable structure are literally translated as "analytic varieties", while spaces with an algebraic structure are called "algebraic varieties". Thus for example, the french word "" means topological manifold. In the same vein, the Japanese word "" (tayōtai) also encompasses both manifold and variety. ("" (tayō) means various.) Ancestral to the modern concept of a manifold were several important results of 18th and 19th century mathematics. The oldest