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Record W2951578430 · doi:10.48550/arxiv.math/0405199

Extension dimension and quasi-finite CW-complexes

2004· preprint· en· W2951578430 on OpenAlexaff
A. Karasev, Vesko Valov

Bibliographic record

VenueArXiv.org · 2004
Typepreprint
Languageen
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsNipissing University
Fundersnot available
KeywordsMetrization theoremMathematicsPure mathematicsExtension (predicate logic)Characterization (materials science)Invertible matrixCountable setClass (philosophy)FactorizationDimension (graph theory)Discrete mathematicsMathematical analysisComputer sciencePhysicsSeparable spaceAlgorithm

Abstract

fetched live from OpenAlex

We extend the definition of quasi-finite complexes by considering not necessarily countable complexes. We provide a characterization of quasi-finite complexes in terms of L-invertible maps and dimensional properties of compactifications. Several results related to the class of quasi-finite complexes are established, such as completion of metrizable spaces, existence of universal spaces and a version of the factorization theorem. Further, we extend the definition of UV(L)-spaces on non-compact case and show that some properties of UV(n)-spaces and UV(n)-maps remain valid, respectively, for UV(L)-spaces and UV(L)-maps.

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)0.001
metaresearch head score (Gemma)0.002
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
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0010.002
Scholarly communication0.0030.005
Open science0.0000.002
Research integrity0.0000.001
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 head0.077
GPT teacher head0.326
Teacher spread0.249 · 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

Citations1
Published2004
Admission routes1
Has abstractyes

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Same venueArXiv.org→Same topicHomotopy and Cohomology in Algebraic Topology→French-language works237,207→