If a linear map is a bijection then it is called a linear isomorphism. A homeomorphism is a bijection that is continuous and whose inverse is also continuous. A bijective function is a bijection (one-to-one correspondence). It follows that the composition of two bijections is also a bijection. Every continuous bijection from a compact space to a Hausdorff space is necessarily a homeomorphism. The image of a computable set under a total computable bijection is computable. Let formula 27 be any continuously differentiable bijection. This relation gives a bijection between involutory matrices and idempotent matrices. Like any other bijection, a global isometry has a function inverse. A function is invertible if and only if it is a bijection. The disjoint union is thus defined up to a bijection. A permutation is simply a bijection from the set of positive integers to itself. There is thus an inclusion-reversing bijection between the projective spaces and . Technically, a permutation of a set is defined as a bijection from to itself. This is an analytic bijection with analytic inverse.