Live briefing
Everything about Surjective function
Mathematical function such that every output has at least one input
In mathematics, a surjective function (also known as surjection, or onto function ) is a function f such that, for every element y of the function's codomain, there exists at least one element x in the function's domain such that f(x) = y. In other words, for a function f : X → Y, the codomain Y is the image of the function's domain X. It is not required that x be unique; the function f may map one or more elements of X to the same element of Y. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Surjective functionA 5-minute orientation
- Skim a recent paper: On stability of almost surjective functional equations of uniformly convex Banach spacesInfluential work since 2022
- Pick up a classic book: Discrete mathematicsThe most-reprinted book on the subject
- Read the landmark paper: Uncountably Generated Algebras of Everywhere Surjective FunctionsCited 15 times
- Go sideways: Bijection, injection and surjectionA closely related topic
- Go sideways: Injective functionA closely related topic
📖 Definitions
Noun Synonym of surjection.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Uncountably Generated Algebras of Everywhere Surjective Functions
LINEAR SURJECTIVE ISOMETRIES BETWEEN VECTOR-VALUED FUNCTION SPACES
Surjective isometries on the vector-valued differentiable function spaces
Surjective isometries on vector-valued differentiable function spaces
Lie groups and subsemigroups with surjective exponential function
Real-linear surjective isometries between function spaces
A Function That Is Surjective on Every Interval
An Almost Everywhere Constant Function Surjective on Every Interval
🆕 Influential since 2022
On stability of almost surjective functional equations of uniformly convex Banach spaces
Bounded Surjective Quadratic Functions over Fnp for MPC-/ZK-/FHE-Friendly Symmetric Primitives
Surjective isometries on a Banach space of analytic functions with bounded derivatives
Surjective Isometries on Function Spaces with Derivatives
Non-surjective coarse embeddings of continuous functions spaces
📚 Books worth reading
Discrete mathematicsNorman Biggs · 1985- 📕Lie groups with surjective exponential functionMichael Wüstner · 2001
MoonshineJames Lepowsky · 2010
MoonshineJames Lepowsky · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Bijection, injection and surjection In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from…
- Injective function In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct…
- Bijection In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between two sets such that each element of the second set (the…
- Morphism In mathematics, a morphism is a concept of category theory that generalizes structure-preserving maps such as homomorphism between algebraic structures…
- Function (mathematics) In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function…
- List of types of functions In mathematics, functions can be identified according to the properties they have. These properties describe the functions' behaviour under certain conditions…
- Epimorphism In category theory, an epimorphism is a morphism f : X → Y that is right-cancellative in the sense that, for all objects Z and all morphisms g1, g2: Y…
- Partial function In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly the whole X itself) to Y. The subset S, that…