Bibliographic record
Abstract
Abstract With the aim of to pologizing domains of matrices with natural topologies, we mainly study FK-spaces in this chapter. These are sequence spaces carrying a metrizable locally convex topology which is complete (F-space) such that convergence implies coordinatewise convergence (K-space). FK-space theory was initiated by K. Zeller in 1949. On the one hand it makes possible the application of functional analytic methods to a number of major problems in summability and, on the other hand, it has proved very fruitful in the development of some topics in functional analysis, for example that of topological sequence spaces. Definitely, the inspiration for FK-space theory came from the Polish school around S. Banach, S. Mazur and W. Orlicz in which functional analytic methods were applied, for instance, to prove the bounded consistency theorem. Around 1949, K. Zeller published some seminal papers, for example, [261], [260], [262]. The subject was then further developed by Zeller and many other mathematicians. Wilansky’s book, [254], traces the development of the subject up to 1984.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot 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.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".