{"schema_version":"ocme-site-results-v1","locale":"en","page_type":"paths","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{},"path":{"id":"path-set-language-to-topology-candidate","title":{"zh-Hant":"集合語言到拓撲前置候選路徑","en":"Set Language toward Topology"},"summary":{"zh-Hant":"從集合、元素隸屬、子集合與基本集合運算建立閱讀拓撲空間定義所需的集合語言。","en":"Build the set-language prerequisites needed to read the definition of a topological space, progressing through sets, membership, subsets, and basic set operations."},"audience":["upper_secondary","undergraduate"],"review":"candidate","nodes":[{"id":"mko-set","position":1,"requirement":"required","rationale":{"zh-Hant":"先確立集合是由隸屬條件刻畫的對象。","en":"Begin with sets as objects characterized by membership conditions."}},{"id":"mko-set-membership","position":2,"requirement":"required","rationale":{"zh-Hant":"再以元素是否屬於集合表達運算定義。","en":"Use element membership to express the definitions of later set operations."}},{"id":"mko-subset","position":3,"requirement":"required","rationale":{"zh-Hant":"由逐元素隸屬建立集合之間的包含關係。","en":"Develop the subset relation between sets from element-wise membership implication."}},{"id":"mko-set-operations","position":3,"requirement":"required","rationale":{"zh-Hant":"平行建立聯集、交集、差集與相對補集。","en":"In parallel, develop union, intersection, difference, and complement relative to an explicit universe."}}]},"title":"Set Language toward Topology"}