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Record W2127866371 · doi:10.1090/s0002-9939-03-06966-1

Perfectly normal non-metrizable non-Archimedean spaces are generalized Souslin lines

2003· article· en· W2127866371 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueProceedings of the American Mathematical Society · 2003
Typearticle
Languageen
FieldMathematics
Topicadvanced mathematical theories
Canadian institutionsUniversity of Toronto
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsMetrization theoremMathematicsPure mathematicsMathematical analysis

Abstract

fetched live from OpenAlex

In this paper we prove the equivalence between the existence of perfectly normal, non-metrizable, non-archimedean spaces and the existence of “generalized Souslin lines", <italic>i.e.,</italic> linearly ordered spaces in which every collection of disjoint open intervals is <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma"> <mml:semantics> <mml:mi> σ </mml:mi> <mml:annotation encoding="application/x-tex">\sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -discrete, but which do not have a <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma"> <mml:semantics> <mml:mi> σ </mml:mi> <mml:annotation encoding="application/x-tex">\sigma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -discrete dense set. The key ingredient is the observation that every first countable linearly ordered space has a dense non-archimedean subspace.

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.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.006
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow)
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 score0.389
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.006
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0020.001
Bibliometrics0.0000.001
Science and technology studies0.0000.002
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0000.000

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 head0.020
GPT teacher head0.293
Teacher spread0.273 · 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