Any function induces a surjection by restricting its codomain to its range. Any function induces a surjection by restricting its codomain to the image of its domain. For example, the inclusion is a ring epimorphism, but not a surjection. In set theory, the term "epimorphism" is synonymous with "surjection", i.e. To be invertible, a function must be both an injection and a surjection. Conversely, if a surjection admits a fibered atlas, then is a fibered manifold. The map "f" is a surjection&colon; each vertex of "H" has a preimage in "C". Similarly, any surjection between two finite sets of the same cardinality is also an injection. Given a module "M", let "P" be a projective module with a surjection formula 3. Every function with a right inverse is necessarily a surjection. Since is an isometric surjection, it is unitary. Any function can be decomposed into a surjection and an injection. Since this is a surjection, the transpose formula 17 is an injection. Let formula 6 and formula 7 be the natural surjection. We define the continuous surjection formula 166 by formula 167.