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alternate case: injective function
Hammer retroazimuthal projection
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the back and front hemispheres overlap, making the projection a non-injective function. The back hemisphere can be rotated 180° to avoid overlap, but inFactorization system (867 words) [view diff] exact match in snippet view article find links to article
written as the composite of a surjective function followed by an injective function. Factorization systems are a generalization of this situation in categoryLocal diffeomorphism (670 words) [view diff] exact match in snippet view article find links to article
smooth immersion is a locally injective function while invariance of domain guarantees that any continuous injective function between manifolds of equalImmersion (mathematics) (2,807 words) [view diff] exact match in snippet view article
Dpf:TpM→Tf(p)N{\displaystyle D_{p}f:T_{p}M\to T_{f(p)}N\,} is an injective function at every point p of M (where TpX denotes the tangent space of a manifoldSection (category theory) (786 words) [view diff] exact match in snippet view article
synonym f;g for g∘f. In the category of sets, every monomorphism (injective function) with a non-empty domain is a section, and every epimorphism (surjectiveDiscrete space (2,287 words) [view diff] exact match in snippet view article find links to article
notation of numbers. (See Cantor space.) Every fiber of a locally injective function is necessarily a discrete subspace of its domain. In the foundationsNumbering (computability theory) (733 words) [view diff] exact match in snippet view article
single-valued if η(x) = η(y) if and only if x=y; in other words if η is an injective function. A single-valued numbering of the set of partial computable functionsRecognizable set (845 words) [view diff] exact match in snippet view article find links to article
\{0\}=\phi ^{-1}(\phi (\{0\}))}, then ϕ{\displaystyle \phi } is an injective function; hence M{\displaystyle M} is infinite. Also, in general, REC(N){\displaystyleDiffeology (2,778 words) [view diff] exact match in snippet view article find links to article
diffeology of X {\displaystyle X} . Similarly, an induction is an injective function f : X → Y {\displaystyle f:X\to Y} between diffeological spaces suchSurface (topology) (4,170 words) [view diff] exact match in snippet view article
equivalent, but their embeddings are not. The image of a continuous, injective function from R2 to higher-dimensional Rn is said to be a parametric surfaceGlossary of Principia Mathematica (1,102 words) [view diff] exact match in snippet view article find links to article
one containing all members of some type vector 1. Essentially an injective function from a class to itself (for example, a vector in a vector space actingLarge countable ordinal (5,516 words) [view diff] exact match in snippet view article find links to article
nonprojectible if there is no total α {\displaystyle \alpha } -recursive injective function mapping α {\displaystyle \alpha } into a smaller ordinal. (This is