- In mathematics, a
surjective function (also
known as
surjection, or onto
function /ˈɒn.tuː/) is a
function f such that, for
every element y of the function's...
- In mathematics, injections,
surjections, and
bijections are
classes of
functions distinguished by the
manner in
which arguments (input
expressions from...
-
Functions which satisfy property (3) are said to be "onto Y " and are
called surjections (or
surjective functions).
Functions which satisfy property (4) are said...
- {\displaystyle h=f\circ g} for a
suitable injection f {\displaystyle f} and
surjection g . {\displaystyle g.} This
decomposition is
unique up to isomorphism...
- The
theorem on the
surjection of Fréchet
spaces is an
important theorem, due to
Stefan Banach, that
characterizes when a
continuous linear operator between...
- equivalently, a
surjection from a set to
another set. The
function from
elements to
equivalence classes is a
surjection, and
every surjection corresponds...
-
which maps each
element to its
equivalence class, is
called the
canonical surjection, or the
canonical projection.
Every element of an
equivalence class characterizes...
- the term
rigid is also used to
define the
notion of a
rigid surjection,
which is a
surjection f : n → m {\displaystyle f:n\to m} for
which the following...
- {\displaystyle \ker(f)} is a
closed set. If f {\displaystyle f} is an open
surjection and ker ( f ) {\displaystyle \ker(f)} is a
closed set then Y {\displaystyle...
- {\displaystyle [x].} The
construction of Y {\displaystyle Y}
defines a
canonical surjection q : X ∋ x ↦ [ x ] ∈ Y . {\textstyle q:X\ni x\mapsto [x]\in Y.} As discussed...
