{"id":"W54369028","doi":"10.1023/a:1008682930706","title":"What is a Quotient Map with Respect to a Closure Operator?","year":2001,"lang":"en","type":"article","venue":"Applied Categorical Structures","topic":"Advanced Topology and Set Theory","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":false,"ca_institutions":"York University","funders":"Centro de Matemática, Universidade de Coimbra; Natural Sciences and Engineering Research Council of Canada","keywords":"Quotient; Mathematics; Closure (psychology); Class (philosophy); Operator (biology); Pure mathematics; Closure operator; Analogy; Equivalence class (music); Topological space; Discrete mathematics; Combinatorics; Closed set; Computer science; Artificial intelligence","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002412278,0.0006415197,0.001060461,0.001992168,0.001779274,0.004569661,0.001027667,0.002056444,0.005501197],"category_scores_gemma":[0.006711148,0.0003489988,0.001110155,0.001204673,0.008552078,0.01859872,0.00250666,0.002695763,0.0008090487],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001082594,"about_ca_system_score_gemma":0.000740729,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009680082,"about_ca_topic_score_gemma":0.0003205054,"domain_scores_codex":[0.9984797,0.0003937893,0.00009295161,0.0003989279,0.0003908612,0.000243795],"domain_scores_gemma":[0.9968284,0.001192292,0.0002668933,0.0003861232,0.0006672521,0.0006590718],"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":[0.00004085805,0.00002069276,0.0002954612,0.00003246218,0.00001116081,0.0001022721,0.0005501864,0.0001341229,0.0009084746,0.9931647,0.000573919,0.004165567],"study_design_scores_gemma":[0.000009424822,0.00002092999,0.0002255226,0.0000116395,0.000009179703,0.0001956034,0.0004352708,0.0006734573,0.0007264434,0.9929742,0.00470502,0.00001336649],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.499257,0.003703011,0.2888991,0.0156461,0.002323785,0.0001237897,0.0005190957,0.0008769032,0.1886511],"genre_scores_gemma":[0.9666705,0.0009705034,0.01734457,0.0007164243,0.000838432,0.0000634668,0.0002332729,0.0002021088,0.01296062],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.005501197,"threshold_uncertainty_score":0.01840341,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02094277057253269,"score_gpt":0.2981253502453908,"score_spread":0.2771825796728581,"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."}}