Nodecness of Soft Generalized Topological Spaces
Bibliographic record
Abstract
In this work, we define a new class of soft generalized topological spaces, namely strongly soft nodec, with the use of strongly soft nowhere dense sets. Then, we study the basic properties of these spaces and show that if the product of two soft generalized topological spaces is a strongly soft nodec space, then each one is a strongly soft nodec space. Then, we extend these notions to T0-strongly soft nodec generalized topological spaces by using the soft quotient functions and discussing their main properties. We also show the inverse of a surjective soft quotient function preserves the soft closure and soft interior of a soft subset of a codomain soft set in soft generalized topological space. Further, we use soft quasi-homeomorphism and soft quotient functions to make comparisons and connections between these spaces with the support of appropriate counterexamples. Then, we successfully determine a condition under which the soft generalized topological space is a soft weak Baire space and hence a strongly soft second category.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".