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A survey of nearisometries

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Jussi Vaisala

Functional Analysis · Submitted 11 Jan 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The present article contains an addendum to the published paper, giving recent results on nearsurjective maps of Banach spaces.

how it is stated · asserted 0.99 read the record →

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arXiv IDmath/0201098 (version 1)
Pith ID727P6ZMP, Pith's permanent record of this paper and its review
CitationJussi Vaisala. "A survey of nearisometries." arXiv:math/0201098 (2002). https://pith.science/paper/727P6ZMP
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,273 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.28 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.56 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Let E and F be Banach spaces, let A be a subset of E, and let s \ge 0. A map f: A -> F is an s-nearisometry if |x-y|-s \le |fx-fy| \le |x-y|+s for all x,y in A. The article gives a survey on the stability problem: How well can an s-nearisometry be approximated by a true isometry? The first result on this problem was given by Hyers and Ulam in 1945 for surjective nearisometries between Hilbert spaces. The present article contains an addendum to the published paper, giving recent results on nearsurjective maps of Banach spaces.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Let E and F be Banach spaces, let A be a subset of E, and let s \ge 0. background 1.00 0.07 0.01 unclear 0.73
s1 A map f: A -> F is an s-nearisometry if |x-y|-s \le |fx-fy| \le |x-y|+s for all x,y in A. background 1.00 0.08 0.03 asserted 0.99
s2 The article gives a survey on the stability problem: How well can an s-nearisometry be approximated by a true isometry? contribution 0.60 0.40 0.14 asserted 0.94
s3 The first result on this problem was given by Hyers and Ulam in 1945 for surjective nearisometries between Hilbert spaces. background 1.00 0.03 0.04 asserted 1.00
s4 The present article contains an addendum to the published paper, giving recent results on nearsurjective maps of Banach spaces. contribution 0.99 0.77 0.10 asserted 0.99

What kind of paper the classifier reports this is: review 0.98 · evidence from literature 0.91.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Let E and F be Banach spaces, let A be a subset of E, and let s \ge 0. A map f: A -> F is an s-nearisometry if |x-y|-s \le |fx-fy| \le |x-y|+s for all x,y in A. The article gives a survey on the stability problem: How well can an s-nearisometry be approximated by a true isometry? The first result on this problem was given by Hyers and Ulam in 1945 for surjective nearisometries between Hilbert spaces. The present article contains an addendum to the published paper, giving recent results on nearsurjective maps of Banach spaces.

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