Bibliographic record
Abstract
The set of compact connected metric spaces (continua) can be divided into classes according to the complexity of their descriptions as inverse limits of polyhedra. The simplest such class is the collection of chainable continua, i.e. those which are inverse limits of arcs. In 1964, A. Lelek introduced a notion which is related to chainability, called span zero. A continuum X has span zero if any two continuous maps from any other continuum to X with identical ranges have a coincidence point. Lelek observed that every chainable continuum has span zero; he later asked whether span zero is in fact a characterization of chainability. In this thesis, we construct a non-chainable continuum in the plane which has span zero, thus providing a counterexample for what is now known as Lelek's Problem in continuum theory. Moreover, we show that the plane contains an uncountable family of pairwise disjoint copies of this continuum. We discuss connections with the classical problem of determining up to homeomorphism all the homogeneous continua in the plane.
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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 | 0.000 |
| 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".