Bibliographic record
Abstract
We give an Ostaszewski-type inductive construction of a locally countable locally compact space which is not α-realcompact but whose onepoint compactification is sequential. This answers a question of Nyikos. The essential ingredient is the use of the Balcar–Vojtas almost-disjoint refinement technique to guide the induction through continuum-many steps. Introduction A subset Y of a space X is sequentially closed if no sequence which is a subset of Y converges to a point outside of Y . A space is sequential if each sequentially closed subset is closed. There are not many absolute examples of ‘complicated’ compact sequential spaces in the literature. Furthermore, several important recent results of Balogh, Fremlin and Nyikos, which use Todorčević's ‘forcing positive partition relations’ techniques, show that such spaces cannot be too complicated. For example, they must contain points of first countability and no subspace can be mapped by a closed map onto ω 1 . The technique, roughly speaking, is to take a countably cpmplete maximal filter of closed sets of a subspace and diagonalize through it with an ω 1 sequence that is homogeneous with respect to a certain partition. The homogeneity with respect to the partition guarantees that the sequence ends up being a free sequence in the sense of Arhangel'skii (see [1] or [6]). The upshot is that there cannot be too many countably complete maximal filters on subspaces.
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.
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 | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.009 | 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 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".