Caribbean hermit crab Caribbean hermit crab The Caribbean hermit crab, Coenobita clypeatus, also known as the soldier crab, the West Atlantic crab, the tree crab, and the purple pincher (due to the distinctive purple claw), is a species of land hermit crab native to the west Atlantic, Bahamas, Belize, southern Florida, Venezuela, the Virgin Islands, and the West Indies. Adults burrow and hide under the roots of large trees, and can be found a considerable distance inland. As with other terrestrial crabs, they utilize modified gills to breathe air. Their shell helps maintain the humidity necessary for gas exchange to function. Caribbean hermit
History of manifolds and varieties History of manifolds and varieties The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are called Lie Groups. Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure, they are called algebraic groups. The term "manifold" comes from German "Mannigfaltigkeit," by Riemann. In English, "manifold" refers to