About: Topologies on spaces of linear maps

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In mathematics, particularly functional analysis, spaces of linear maps between two vector spaces can be endowed with a variety of topologies. Studying space of linear maps and these topologies can give insight into the spaces themselves. The article operator topologies discusses topologies on spaces of linear maps between normed spaces, whereas this article discusses topologies on such spaces in the more general setting of topological vector spaces (TVSs).

Attributes	Values
rdf:type	Thing
rdfs:label	균등 수렴 위상 (ko) Topologies on spaces of linear maps (en)
rdfs:comment	In mathematics, particularly functional analysis, spaces of linear maps between two vector spaces can be endowed with a variety of topologies. Studying space of linear maps and these topologies can give insight into the spaces themselves. The article operator topologies discusses topologies on spaces of linear maps between normed spaces, whereas this article discusses topologies on such spaces in the more general setting of topological vector spaces (TVSs). (en) 해석학에서 균등 수렴 위상(均等收斂位相, 영어: topology of uniform convergence)은 일반위상수학적인 극한이 균등 수렴과 일치하게 하는, 함수 공간 위의 위상이다. 이 경우, 공역에 위상 벡터 공간 또는 (보다 일반적으로) 균등 공간 구조가 필요하다. 만약 공역에 거리 공간이나 노름 공간과 같은 구조가 주어지면, 이 위상 및 균등 공간 구조와 호환되는 균등 거리 함수(영어: uniform metric) 및 균등 노름(영어: uniform norm)을 정의할 수 있다. (ko)
rdfs:seeAlso	Uniform space
name	Theorem (en)
dct:subject	Topological vector spaces Functional analysis Topology of function spaces
Wikipage page ID	41677409 (xsd:integer)
Wikipage revision ID	1108332991 (xsd:integer)
Link from a Wikipage to another Wikipage	Product topology Quasi-complete Montel space Barrelled space Bornological space Bounded set (topological vector space) Topological vector spaces Uniform space Vector space Complete topological vector space Completely regular space Complex numbers Convex set Mathematics Separable space Quasi-complete space Fréchet space Operator topologies Dense set Functional analysis Mackey topology Balanced set Topological vector space Topology (structure) Weak topology Hausdorff space Linear map Linear span Absolutely convex set Dual space F-space Absolutely convex Normed space Directed set Baire space Tensor product Absorbing set Functional analysis LF-space Topology of function spaces Bornology Polar topology Metrizable TVS Neighbourhood system Net (mathematics) Real numbers Saturated family Locally convex Total set Strong dual space Equicontinuous linear functionals Equicontinuous linear maps Barreled space Filter base Minkowski sum
sameAs	Topologies on spaces of linear maps Topologies on spaces of linear maps Topologies on spaces of linear maps
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has abstract	In mathematics, particularly functional analysis, spaces of linear maps between two vector spaces can be endowed with a variety of topologies. Studying space of linear maps and these topologies can give insight into the spaces themselves. The article operator topologies discusses topologies on spaces of linear maps between normed spaces, whereas this article discusses topologies on such spaces in the more general setting of topological vector spaces (TVSs). (en) 해석학에서 균등 수렴 위상(均等收斂位相, 영어: topology of uniform convergence)은 일반위상수학적인 극한이 균등 수렴과 일치하게 하는, 함수 공간 위의 위상이다. 이 경우, 공역에 위상 벡터 공간 또는 (보다 일반적으로) 균등 공간 구조가 필요하다. 만약 공역에 거리 공간이나 노름 공간과 같은 구조가 주어지면, 이 위상 및 균등 공간 구조와 호환되는 균등 거리 함수(영어: uniform metric) 및 균등 노름(영어: uniform norm)을 정의할 수 있다. (ko)
math statement	Let be a non-empty collection of bounded subsets of Then the -topology on is not altered if is replaced by any of the following collections of subsets of : all subsets of all finite unions of sets in ; all scalar multiples of all sets in ; all finite Minkowski sums of sets in ; the balanced hull of every set in ; the closure of every set in ; and if and are locally convex, then we may add to this list: the closed convex balanced hull of every set in (en) If and if is a net in then in the -topology on if and only if for every converges uniformly to on (en) The -topology on is compatible with the vector space structure of if and only if every is -bounded; that is, if and only if for every and every is bounded in (en)
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page length (characters) of wiki page	38089 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Topologies_on_spaces_of_linear_maps
is Link from a Wikipage to another Wikipage of	Bornological space Complete topological vector space Topology of uniform convergence Weak topology

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