- and only if it is both
surjective and injective. If (as is
often done) a
function is
identified with its graph, then
surjectivity is not a
property of the...
-
notion of point-
surjectivity can be defined. A
morphism f : X → B A {\displaystyle f:X\rightarrow B^{A}} is said to be
weakly point-
surjective if for every...
- {\displaystyle \forall x,x'\in X,x\neq x'\implies f(x)\neq f(x').} The
function is
surjective, or onto, if each
element of the
codomain is
mapped to by at
least one...
-
epimorphism (
surjective) ⟹
epimorphism (right cancelable) ; {\displaystyle {\text{split epimorphism}}\implies {\text{epimorphism (
surjective)}}\implies...
-
category theory, a
functor F : C → D {\displaystyle F:C\to D} is
essentially surjective if each
object d {\displaystyle d} of D {\displaystyle D} is isomorphic...
-
projection in a
smooth vector bundle or a more
general smooth fibration. The
surjectivity of the
differential is a
necessary condition for the
existence of a local...
-
categorical analogues of onto or
surjective functions (and in the
category of sets the
concept corresponds exactly to the
surjective functions), but they may...
- mathematics, the Ax–Grothendieck
theorem is a
result about injectivity and
surjectivity of
polynomials that was
proved independently by
James Ax and Alexander...
-
homomorphism between two
algebraic structures is an embedding.
Unlike surjectivity,
which is a
relation between the
graph of a
function and its codomain...
- In
functional analysis, a
unitary operator is a
surjective bounded operator on a
Hilbert space that
preserves the
inner product.
Unitary operators are...
