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Record W2314725449 · doi:10.4153/cmb-2000-028-0

Extensions of Continuous and Lipschitz Functions

2000· article· en· W2314725449 on OpenAlexvenueno aff
Eva Matoušková

Bibliographic record

VenueCanadian Mathematical Bulletin · 2000
Typearticle
Languageen
FieldMathematics
TopicAdvanced Banach Space Theory
Canadian institutionsnot available
Fundersnot available
KeywordsMathematicsLipschitz continuityLipschitz domainUniform continuityBounded functionContinuous function (set theory)Norm (philosophy)Uniform normPure mathematicsMetric differentialInfimum and supremumBanach spaceMetric spaceHausdorff spaceDiscrete mathematicsFunction (biology)Mathematical analysisMetric mapInjective metric space

Abstract

fetched live from OpenAlex

Abstract We show a result slightly more general than the following. Let K be a compact Hausdorff space, F a closed subset of K , and d a lower semi-continuous metric on K . Then each continuous function ƒ on F which is Lipschitz in d admits a continuous extension on K which is Lipschitz in d . The extension has the same supremum norm and the same Lipschitz constant. As a corollary we get that a Banach space X is reflexive if and only if each bounded, weakly continuous and norm Lipschitz function defined on a weakly closed subset of X admits a weakly continuous, norm Lipschitz extension defined on the entire space X .

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.006
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.003
Threshold uncertainty score0.011

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.006
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0010.001
Science and technology studies0.0010.003
Scholarly communication0.0020.005
Open science0.0010.003
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0030.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.015
GPT teacher head0.248
Teacher spread0.233 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations20
Published2000
Admission routes1
Has abstractyes

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Same venueCanadian Mathematical BulletinSame topicAdvanced Banach Space TheoryFrench-language works237,207