{"id":"W4406489791","doi":"10.48550/arxiv.2408.01870","title":"On uniformly continuous surjections between $C_p$-spaces over metrizable spaces","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Türkiye Bilimsel ve Teknolojik Araştırma Kurumu","keywords":"Bijection, injection and surjection; Metrization theorem; Mathematics; Pure mathematics; Combinatorics; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0004251116,0.0004921809,0.0007319929,0.0006390119,0.0002841149,0.00008640331,0.000582976,0.0006955773,0.0003632758],"category_scores_gemma":[0.0003199591,0.0005067024,0.0003689164,0.0006595707,0.0003294992,0.000137194,0.0009599809,0.001551031,0.0003703811],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002783146,"about_ca_system_score_gemma":0.00015245,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001371058,"about_ca_topic_score_gemma":0.0001423386,"domain_scores_codex":[0.9979403,0.000221715,0.0002717387,0.0009649164,0.0001135266,0.0004878211],"domain_scores_gemma":[0.9970126,0.001515129,0.0002889217,0.0009091963,0.0001073076,0.0001668872],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00009104567,0.000112079,0.001723194,0.0002635271,0.0005872606,0.0002930428,0.000252611,0.006489167,0.000009199378,0.9871169,0.002988028,0.00007394436],"study_design_scores_gemma":[0.0004216885,0.0001186626,0.0001619374,0.0002424713,0.0006254009,0.000004346879,0.0005581443,0.001119622,0.0002067571,0.9936968,0.002314262,0.0005299214],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9289587,0.0002030031,0.02417775,0.0001579379,0.001131619,0.000484647,0.0002637641,0.0006575367,0.04396509],"genre_scores_gemma":[0.9572078,0.0001389555,0.0004659771,0.00004514113,0.0001992716,0.000002077476,0.000042534,0.00006778519,0.04183044],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02824917,"threshold_uncertainty_score":0.9997385,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0903753059809562,"score_gpt":0.2494657277274603,"score_spread":0.1590904217465041,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}