the back and front hemispheres overlap, making the projection a non-injectivefunction. The back hemisphere can be rotated 180° to avoid overlap, but in
written as the composite of a surjective function followed by an injectivefunction. Factorization systems are a generalization of this situation in category
→ T f ( p ) N {\displaystyle D_{p}f:T_{p}M\to T_{f(p)}N\,} is an injectivefunction at every point p of M (where TpX denotes the tangent space of a manifold
smooth immersion is a locally injectivefunction, while invariance of domain guarantees that any continuous injectivefunction between manifolds of equal
{\displaystyle g\circ f} . In the category of sets, every monomorphism (injectivefunction) with a non-empty domain is a section, and every epimorphism (surjective
notation of numbers. (See Cantor space.) Every fiber of a locally injectivefunction is necessarily a discrete subspace of its domain. In the foundations
single-valued if η(x) = η(y) if and only if x=y; in other words if η is an injectivefunction. A single-valued numbering of the set of partial computable functions
\{0\}=\phi ^{-1}(\phi (\{0\}))} , then ϕ {\displaystyle \phi } is an injectivefunction; hence M {\displaystyle M} is infinite. Also, in general, R E C (
equivalent, but their embeddings are not. The image of a continuous, injectivefunction from R2 to higher-dimensional Rn is said to be a parametric surface
diffeology of X {\displaystyle X} . Similarly, an induction is an injectivefunction f : X → Y {\displaystyle f:X\to Y} between diffeological spaces such
one containing all members of some type vector 1. Essentially an injectivefunction from a class to itself (for example, a vector in a vector space acting