Schreier family in Banach space theory
E1212017
UNEXPLORED
The Schreier family in Banach space theory is a combinatorial collection of finite subsets of natural numbers introduced by Józef Schreier that plays a central role in constructing and analyzing special Banach spaces with unusual structural properties.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Schreier family in Banach space theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T16411742 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Schreier family in Banach space theory Context triple: [Józef Schreier, notableWork, Schreier family in Banach space theory]
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A.
Gowers dichotomy for Banach spaces
Gowers dichotomy for Banach spaces is a fundamental result in functional analysis that classifies infinite-dimensional Banach spaces by showing that each contains either a subspace with an unconditional basis or a hereditarily indecomposable subspace.
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B.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
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C.
Gowers–Maurey space
The Gowers–Maurey space is a specially constructed Banach space that provided a counterexample to the unconditional basic sequence problem, showing that there exist Banach spaces with no unconditional basic sequences.
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D.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
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E.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Schreier family in Banach space theory Target entity description: The Schreier family in Banach space theory is a combinatorial collection of finite subsets of natural numbers introduced by Józef Schreier that plays a central role in constructing and analyzing special Banach spaces with unusual structural properties.
-
A.
Gowers dichotomy for Banach spaces
Gowers dichotomy for Banach spaces is a fundamental result in functional analysis that classifies infinite-dimensional Banach spaces by showing that each contains either a subspace with an unconditional basis or a hereditarily indecomposable subspace.
-
B.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
-
C.
Gowers–Maurey space
The Gowers–Maurey space is a specially constructed Banach space that provided a counterexample to the unconditional basic sequence problem, showing that there exist Banach spaces with no unconditional basic sequences.
-
D.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
-
E.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.