{"id":"W4411151718","doi":"10.1515/ms-2025-0049","title":"Linear and uniformly continuous surjections between <i>C<sub>p</sub> </i>-spaces over metrizable spaces","year":2025,"lang":"en","type":"article","venue":"Mathematica Slovaca","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Nipissing University","funders":"","keywords":"Mathematics; Metrization theorem; Surjective function; Pointwise; Bijection, injection and surjection; Bounded function; Tychonoff space; Uniform continuity; Countable set; Space (punctuation); Pointwise convergence; Discrete mathematics; Function space; Continuous function (set theory); Combinatorics; Pure mathematics; Topological space; Mathematical analysis; Function (biology); Metric space; Separable space","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.0006382699,0.0003438353,0.0007671484,0.0003492601,0.0003892917,0.00007698189,0.0002576329,0.0002806446,0.00008688965],"category_scores_gemma":[0.001202476,0.000297517,0.0001336054,0.0006274629,0.0003430847,0.0002395324,0.0002067006,0.0003885787,0.00007205721],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004692109,"about_ca_system_score_gemma":0.00005903744,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000005811624,"about_ca_topic_score_gemma":0.00001756612,"domain_scores_codex":[0.9982226,0.0001368583,0.0005424878,0.0004093584,0.0002183184,0.0004704087],"domain_scores_gemma":[0.9964204,0.002582254,0.0002207152,0.0005567763,0.0001006553,0.0001192107],"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":[0.00005129701,0.000256307,0.001820156,0.0008220294,0.000470513,0.00001617573,0.001143212,0.000006109855,0.004559933,0.9822544,0.006689236,0.001910641],"study_design_scores_gemma":[0.000815946,0.00007712314,0.0003295408,0.0002497757,0.0003377111,0.0000191263,0.001051941,0.0002066333,0.03418569,0.9566563,0.005703542,0.0003666756],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9116591,0.0006491901,0.0590749,0.0008778007,0.0002141269,0.0006124324,0.00003759583,0.0003941308,0.0264807],"genre_scores_gemma":[0.9699947,0.0001657792,0.02353196,0.0002214655,0.0001393385,0.00006752874,0.00001229755,0.00006260158,0.005804351],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05833556,"threshold_uncertainty_score":0.9999477,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01995161111862027,"score_gpt":0.3052351134225205,"score_spread":0.2852835023039003,"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."}}