Open Questions: Glossary of Mathematics

Abelian group
See group.
Abelian variety
Algebra
Algebraic function
Algebraic geometry
Algebraic integer
Algebraic number theory
Algebraic variety
Algebraically closed field
Analytic function
Analytic number theory
Analysis
Automorphic function
Banach space
Boolean algebra
Cartesian product
Category
Cauchy sequence
Chaos
Class field theory
Closed set
Cohomology
Compact
Complete topological space
Complex analysis
Complex numbers
Composition law
A function that takes a pair of elements of some set to some other element of the set. If the pair (a,b) corresponds to c under this function, the law may be written as a ∘ b = c.
Connection
Continuous function
Convergence
Cusp form
Derivative
Diagram
Differentiable function
Differentiable manifold
Differential equation
Differential form
Diophantine equation
Direct product
Direct sum
Dirichlet series
Dynamical system
Elliptic curve
Extension field
Fiber bundle
Field
Fractal
Function
A correspondence between elements of two sets A and B (that may be the same). The correspondence can be defined by a set of ordered pairs of the form (a,b) with a ∈ A and b ∈ B such that there is exactly one a ∈ A that is the first element of any pair. The set A is called the "domain" of the function, while the "range" of the function consists of all b ∈ B that occur as the second element of a pair. A function is usually denoted symbolically with a name such as "f" and written in the form f(a) = b if (a,b) is a pair of corresponding elements. A function is "injective" or "1-to-1" if there is no b ∈ B that occurs more than once as the second element of a pair. (I. e., f(a) = f(a′) implies a = a′.) A function is "surjective" or "onto" if the range of the function is all of B. (I. e. for all b ∈ B, b = f(a) for some a ∈ A.)
Functional analysis
Galois group
Group
A mathematical system G consiting of a set of elements and a composition law satisfying three axioms: A group is "commutative" or "abelian" if in addition one has
Group representation
Harmonic analysis
Hilbert space
Holomorphic function
Homology
Homeomorphism
Homomorphism
Homotopy
Hopf algebra
Inner product
Integral equations
Isomorphism
Knot
L-function
Lattice
Lie algebra
Lie group
Linear algebra
Manifold
Mapping
Synonym of function.
Matrix
Meromorphic function
Metric space
Modular form
Modular function
Modular group
Morphism
Neighborhood
Normed linear space
Open set
P-adic numbers
Projective plane
Partial differential equation
Pole
Quantum group
Riemann sphere
Riemann surface
Ring
Ring of integers
Series
Sheaf
Tangent bundle
Taylor series
Tensor
Topology
Variety
Vector
Vector bundle
Vector space

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