Continua which admit only certain classes of onto mappings
Bibliographic record
Abstract
The purpose of this article is to present a rather com plete study of those classes of continua which admit only confluent (resp. semi-confluent, weakly confluent, pseudo-confluent) onto mappings. The first results were obtained by H. Cook [3] who proved that if X is a hereditarily inde composable continuum, then every mapping from any continuum onto X is confluent, and by D. R. Read [20] who proved that the converse is true, that is, if X is a continuum such that every mapping from any continuum onto X is confluent, then X is hereditarily indecomposable. In what follows we study the class of continua X with the property that every mapping from any continuum onto X is weakly confluent. Finally, at the end of the paper we study the classes of continua X with the property that every mapping from any continuum onto X is semi-confluent (resp., pseudo-confluent>. 1. Definitions and Preliminaries By a continuum is meant a connected, compact, metric space. By a mapping is always meant a continuous function. A mapping f: X ~ Y of a continuum X onto a continuum Y is said to be confluent [2], semi-confluent [18], or weakly lThe first author was supported by a University of Saskatchewan postdoctoral fellowship. The second author was
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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 | 0.000 | 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) | 0.000 | 0.000 |
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.
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".