In mathematics, specifically in order theory and functional analysis, the order topology of an ordered vector space ( X , ≤ ) {\displaystyle (X,\leq )}...

mathematics, an order topology is a specific topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real...

function spaces carrying a topology; the best known examples include Hilbert spaces and Banach spaces. In functional analysis, the set of all functions...

f^{-1}(y)} is a connected subspace of X . {\displaystyle X.} In functional analysis on a topological vector space X {\displaystyle X} , a (possibly non-linear)...

Arzelà–Ascoli theorem (functional analysis) Baire category theorem (topology, metric spaces) Bing metrization theorem (general topology) Bolzano–Weierstrass...

In mathematics, specifically in order theory and functional analysis, the order dual of an ordered vector space X {\displaystyle X} is the set Pos ⁡ (...

Hausdorff space into a uniform space to be compact in the compact-open topology; see Kelley (1991, page 234). By definition, a sequence { f n } n ∈ N {\displaystyle...

In mathematics, particularly in functional analysis, the closed graph theorem is a result connecting the continuity of a linear operator to a topological...

In topology and related branches of mathematics, total-boundedness is a generalization of compactness for circumstances in which a set is not necessarily...

mathematics, topological data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from...

order summable sequences is related to the completeness of the order topology. Ordered topological vector space Order topology (functional analysis) –...

can refer to: Compact space, in topology Compact operator, in functional analysis Compactness theorem, in first-order logic Compactness measure of a shape...

In functional analysis and related areas of mathematics a polar topology, topology of G {\displaystyle {\mathcal {G}}} -convergence or topology of uniform...

specifically in functional analysis, a positive linear functional on an ordered vector space ( V , ≤ ) {\displaystyle (V,\leq )} is a linear functional f {\displaystyle...

In mathematics, in the field of functional analysis, a Minkowski functional (after Hermann Minkowski) or gauge function is a function that recovers a...

stochastic processes. Set-valued analysis – applies ideas from analysis and topology to set-valued functions. Convex analysis, the study of convex sets and...

≤). The finest order consistent topology is the Scott topology, which is coarser than the Alexandrov topology. A third important topology in this spirit...

targets Operator algebra – Branch of functional analysis Operator theory – Mathematical field of study Topologies on the set of operators on a Hilbert...

abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space that is also a topological...

differential topology, functional analysis and singularity theory, the Whitney topologies are a countably infinite family of topologies defined on the...

In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace...

Kelley, John L. (1975). General Topology. Springer. ISBN 0-387-90125-6. Kreyszig, Erwin, Introductory functional analysis with applications (Wiley, New...

result—maybe the most important fact about the weak-* topology—[that] echos throughout functional analysis.” In 1912, Helly proved that the unit ball of the...

In mathematics, more specifically in functional analysis, a Banach space (/ˈbɑː.nʌx/, Polish pronunciation: [ˈba.nax]) is a complete normed vector space...

consist of a single element. In functional analysis, the strong dual topology is often the "standard" or "default" topology placed on the continuous dual...

was an American mathematician who contributed to real analysis, functional analysis, topology and the study of Boolean algebras. Stone was the son of...

Noncommutative harmonic analysis see representation theory Noncommutative topology Nonlinear analysis Nonlinear functional analysis Number theory a branch...

especially normed linear spaces, in the early days of functional analysis. General topology assumed its present form around 1940. It captures, one might...

and functional analysis that can be carried out in a computable manner. The field is closely related to constructive analysis and numerical analysis. A...

In mathematics, specifically in functional analysis and order theory, an ordered topological vector space, also called an ordered TVS, is a topological...