{"id":"W4388321717","doi":"10.1093/oso/9780198501657.003.0006","title":"Functional analytic basis","year":2000,"lang":"en","type":"book-chapter","venue":"","topic":"Optimization and Variational Analysis","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Western University","funders":"","keywords":"Mathematics; Baire category theorem; Section (typography); Open mapping theorem (functional analysis); Banach space; Metric space; Mathematical proof; Basis (linear algebra); Pure mathematics; Topological space; Fréchet space; Interpolation space; Eberlein–Šmulian theorem; Discrete mathematics; Algebra over a field; Functional analysis; Lp space; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003216781,0.0004939743,0.0003718104,0.0008694196,0.0004525002,0.001442596,0.0004944378,0.0006020571,0.01949472],"category_scores_gemma":[0.0005115041,0.0001448325,0.0003214356,0.0005513303,0.000829752,0.001244916,0.0007850882,0.001093063,0.003394725],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007968344,"about_ca_system_score_gemma":0.0003006912,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006890853,"about_ca_topic_score_gemma":0.0005560648,"domain_scores_codex":[0.9998154,0.00004290083,0.000007671454,0.00003637365,0.00007973913,0.00001800398],"domain_scores_gemma":[0.9998541,0.00003335137,0.000008482878,0.00001841288,0.0000682532,0.00001740208],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00000181769,0.000003893553,0.00002159514,0.00003053488,0.000002935789,0.00001593269,0.00003200602,0.0008807335,0.0004945462,0.9856001,0.004527512,0.008388404],"study_design_scores_gemma":[0.00000237591,0.00001323087,0.0001664085,0.00004437508,0.000004102453,0.00009867883,0.0000532944,0.01411078,0.0004099117,0.9022042,0.08288608,0.000006531176],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.01494188,0.008432155,0.2543281,0.003382415,0.000902019,0.00004906735,0.0005793063,0.0002957391,0.7170894],"genre_scores_gemma":[0.5070168,0.01082087,0.0815092,0.001260863,0.001359221,0.0002063117,0.001065801,0.0003383909,0.3964225],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.01949472,"threshold_uncertainty_score":0.0652163,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02086590770552969,"score_gpt":0.2040801340135772,"score_spread":0.1832142263080475,"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."}}