Bibliographic record
Abstract
Abstract We study the existence of continuity points for mappings whose x-sections are fragmentable and y-sections are quasicontinuous, where X is a Baire space and Z is a metric space. For the factor Y, we consider two infinite “pointpicking” games G 1 (y) and G 2 (y) defined respectively for each y ∈ Y as follows: in the n-th inning, Player I gives a dense set D n ⊂ Y, respectively, a dense open set D n ⊂ Y. Then Player II picks a point y n ∈ D n ; II wins if y is in the closure of {y n : n ∈ N}, otherwise I wins. It is shown that (i) f is cliquish if II has a winning strategy in G 1 (y) for every y ∈ Y, and (ii) f is quasicontinuous if the x-sections of f are continuous and the set of y ∈ Y such that II has a winning strategy in G 2 (y) is dense in Y. Item (i) extends substantially a result of Debs and item (ii) indicates that the problem of Talagrand on separately continuous maps has a positive answer for a wide class of “small” compact spaces.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.015 | 0.001 |
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 teacher head, 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".