{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:6dbf77e2-01b5-48e1-8fc5-8ff5b9354b60",
  "labels": {
    "zh-CN": "拓扑子群",
    "en": "topological subgroup"
  },
  "alternative_labels": [],
  "scope_note": "",
  "identity_status": "active",
  "identity_revision": "87a563c7211458dbdc0b5b11b472e230d321caf869a25dbebb4a6e6574e3c502",
  "occurrences": [
    {
      "concept_id": "urn:uuid:6dbf77e2-01b5-48e1-8fc5-8ff5b9354b60",
      "book_id": "szekeres",
      "edition_id": "source-snapshot-bc3404156f6e",
      "lang": "zh-CN",
      "route": "zh/chapter-10/08-topological-groups",
      "anchor": "first-282ff3f2873eae096c4c-zh",
      "chapter": "10",
      "section": "10.8",
      "offset": 3184,
      "range": [
        7520,
        7765
      ],
      "source_revision": "40e39c23ad4632d9a97f04f151312b72ae74facf203e5c4311357aeafe0559dc",
      "source_category": "translation",
      "review_status": "unreviewed",
      "role": "occurrence",
      "role_basis": {
        "kind": "explicit-source-uuid-marker"
      },
      "label": "拓扑子群(topological subgroup)",
      "context": {
        "range": [
          7490,
          8452
        ],
        "quote": "群 $H$ 的子群 $G$ 连同其相对拓扑称为 $G$ 的 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:6dbf77e2-01b5-48e1-8fc5-8ff5b9354b60\" data-concept-route=\"/concept-identities#concept-6dbf77e2-01b5-48e1-8fc5-8ff5b9354b60\" id=\"first-282ff3f2873eae096c4c-zh\">拓扑子群(topological subgroup)</u>。为证明任意子群 $H$ 关于相对拓扑成为拓扑子群，设 $U ^ { \\prime } = H \\cap U$，其中 $U$ 是 $G .$ 的任意开子集。由映射 $\\phi$ 的连续性，对任意一对满足 $g h \\in U ^ { \\prime } \\subset U$ 的点 $g , h \\in H$，存在 $G$ 的开集 $A$ 和 $B$，使得 $A \\times B \\subset \\phi ^ { - 1 } ( U )$。由此推出 $\\phi ( A ^ { \\prime } \\times B ^ { \\prime } ) \\subset H \\cap U$，其中 $A ^ { \\prime } = A \\cap H$，$B ^ { \\prime } = B \\cap H$，并且 $\\left. \\phi \\right| _ { H }$ 的连续性是直接的。类似地，逆映射 $\\tau$ 限制在 $H$ 上时连续。若 $H$ 是 $G$ 中的闭集，则称其为 $G$ 的 <u class=\"concept-term\" data-concept-identity=\"urn:uuid:03eb86c3-86f8-40cb-8e28-d7d053422767\" data-concept-route=\"/concept-identities#concept-03eb86c3-86f8-40cb-8e28-d7d053422767\" id=\"first-0be35a567ad49081ee79-zh\">闭子群(closed subgroup)</u>。",
        "quote_sha256": "da288dafa542dfb428b6b09d832ad6c7a475636a27b8c5b883a4c346c589c501",
        "environment": null,
        "excerpt_omitted": false
      },
      "parallel_readings": [
        {
          "route": "en/chapter-10/08-topological-groups",
          "lang": "en",
          "source_category": "original_transcription",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-74a15dd43967989a4a907cc9"
    }
  ],
  "registered_positions": [
    {
      "route": "zh/chapter-10/08-topological-groups",
      "lang": "zh-CN",
      "section": "10.8",
      "signal": "term-mark",
      "label": "拓扑子群",
      "english": "topological subgroup",
      "offset": 2802
    }
  ],
  "statements": [],
  "resolved_references": [],
  "reading_order": [
    "occ-74a15dd43967989a4a907cc9"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 1,
    "located_occurrences": 1,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "base_revision": "374bf7db032ba4746a436dd139140b06b657261133d3176941091fcdb1a78b14",
  "optional_enrichments": []
}