47 relations: Abelian group, Absolutely convex set, Algebra over a field, Associative algebra, Banach algebra, Binomial coefficient, Commutative ring, Compact convergence, Compact space, Complex number, Complex plane, Continuous function, Countable set, Derivative, Differentiable manifold, Dimension, Discrete space, Existential quantification, F-space, Finitely generated group, Fréchet space, Functional analysis, Fundamental theorem of calculus, Gδ set, Group algebra, Holomorphic function, Identity element, Inverse limit, Lebesgue measure, Length function, Locally convex topological vector space, Lp space, Mathematics, Maurice René Fréchet, Monotonic function, N-sphere, Natural number, Neighbourhood (mathematics), Norm (mathematics), Open set, Product rule, Real number, Sequence space, Topological algebra, Uniform convergence, Unit (ring theory), Universal quantification.
In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.
A set C in a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (circled), in which case it is called a disk.
In mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product.
In mathematics, an associative algebra is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field.
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach space, i.e. a normed space and complete in the metric induced by the norm.
In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.
In ring theory, a branch of abstract algebra, a commutative ring is a ring in which the multiplication operation is commutative.
In mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence which generalizes the idea of uniform convergence.
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense.
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".
In functional analysis, an F-space is a vector space V over the real or complex numbers together with a metric d: V × V → R so that.
In algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination (under the group operation) of finitely many elements of the finite set S and of inverses of such elements.
In functional analysis and related areas of mathematics, Fréchet spaces, named after Maurice Fréchet, are special topological vector spaces.
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function with the concept of integrating a function.
In the mathematical field of topology, a Gδ set is a subset of a topological space that is a countable intersection of open sets.
In mathematics, the group algebra is any of various constructions to assign to a locally compact group an operator algebra (or more generally a Banach algebra), such that representations of the algebra are related to representations of the group.
In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighborhood of every point in its domain.
In mathematics, an identity element or neutral element is a special type of element of a set with respect to a binary operation on that set, which leaves other elements unchanged when combined with them.
In mathematics, the inverse limit (also called the projective limit or limit) is a construction that allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects.
In measure theory, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of n-dimensional Euclidean space.
In the mathematical field of geometric group theory, a length function is a function that assigns a number to each element of a group.
In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) that generalize normed spaces.
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
Maurice Fréchet (2 September 1878 – 4 June 1973) was a French mathematician.
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.
In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
In topology, an open set is an abstract concept generalizing the idea of an open interval in the real line.
In calculus, the product rule is a formula used to find the derivatives of products of two or more functions.
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
In functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers.
In mathematics, a topological algebra A is an algebra and at the same time a topological space, where the algebraic and the topological structures are coherent in a specified sense.
In the mathematical field of analysis, uniform convergence is a type of convergence of functions stronger than pointwise convergence.
In mathematics, an invertible element or a unit in a (unital) ring is any element that has an inverse element in the multiplicative monoid of, i.e. an element such that The set of units of any ring is closed under multiplication (the product of two units is again a unit), and forms a group for this operation.
In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all".