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gptkbp:instanceOf
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gptkb:mathematical_concept
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gptkbp:application
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gptkb:probability_theory
analysis
partial differential equations
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gptkbp:category
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gptkb:Vector
gptkb:topology
topological vector space
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gptkbp:defines
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A complete normed vector space
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gptkbp:example
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gptkb:Hilbert_space
gptkb:Lp_space
sequence space
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gptkbp:field
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functional analysis
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gptkbp:generalizes
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gptkb:normed_vector_space
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gptkbp:hasProperty
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completeness
linear structure
metric induced by norm
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gptkbp:hasSubfield
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finite-dimensional Banach space
infinite-dimensional Banach space
reflexive Banach space
separable Banach space
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https://www.w3.org/2000/01/rdf-schema#label
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Banach spaces
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gptkbp:introducedIn
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1920s
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gptkbp:namedAfter
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gptkb:Stefan_Banach
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gptkbp:property
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every Cauchy sequence converges
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gptkbp:relatedTo
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gptkb:Banach–Steinhaus_theorem
gptkb:Hahn–Banach_theorem
gptkb:Closed_graph_theorem
gptkb:Open_mapping_theorem
gptkb:Uniform_boundedness_principle
gptkb:Banach–Alaoglu_theorem
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gptkbp:structure
|
gptkb:standard
scalar multiplication
vector addition
|
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gptkbp:usedIn
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gptkb:signal_processing
harmonic analysis
operator theory
quantum mechanics
optimization
|
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gptkbp:bfsParent
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gptkb:Jean_Bourgain
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gptkbp:bfsLayer
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4
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