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LF-space

In mathematics, an LF-space, also written (LF)-space, is a topological vector space (TVS) X that is a locally convex inductive limit of a countable inductive system ( X n , i n m ) {\displaystyle (X_{n},i_{nm})} of Fréchet spaces. This means that X is a direct limit of a direct system ( X n , i n m ) {\displaystyle (X_{n},i_{nm})} in the category of…

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Map overview Semantic statistics

LF-space

Nodes70
Edges69
Triples30
Avg. degree1.97
Density0.028571
Components1

How this topic connects Entity context

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LF-space

Top relations

related to Direct limit of finite-dimensional spaces · 14
LF-space → Also, Denote, Hamel, In, It, LC, Since, Suppose, The, TOP, TVS, Xm, Xm's, Xn
related to LF-spaces · 9
LF-space → Alexander Grothendieck, An LF-space, Every LF-space, Fréchet, If, In, LF, The, Xn
related to Space of smooth compactly supported functions · 5
LF-space → Fréchet, Such, The, The LF-space, With
is a · 2
LF-space → Fréchet space if and only if it is an LB-space, meager subset of itself

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Important terminology

spaces topological isbn displaystyle oclc vector topology limit category direct space xi locally convex inductive fréchet system every new york

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
LF-spaceis ameager subset of itself0.90text
LF-spaceis aFréchet space if and only if it is an LB-space0.90text
LF-spacerelated to Direct limit of finite-dimensional spacesSuppose0.60section
LF-spacerelated to Direct limit of finite-dimensional spacesXn0.60section
LF-spacerelated to Direct limit of finite-dimensional spacesXm0.60section
LF-spacerelated to Direct limit of finite-dimensional spacesDenote0.60section
LF-spacerelated to Direct limit of finite-dimensional spacesSince0.60section
LF-spacerelated to Direct limit of finite-dimensional spacesTVS0.60section
LF-spacerelated to Direct limit of finite-dimensional spacesXm's0.60section
LF-spacerelated to Direct limit of finite-dimensional spacesHamel0.60section
LF-spacerelated to Direct limit of finite-dimensional spacesIt0.60section
LF-spacerelated to Direct limit of finite-dimensional spacesLC0.60section

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