{
  "schema_version": 1,
  "kind": "ConceptView",
  "producer": "concept-view-1",
  "concept_id": "urn:uuid:60b34861-2f0d-55d9-870b-0057366b7436",
  "labels": {
    "zh-CN": "收缩映射",
    "en": "retraction"
  },
  "alternative_labels": [],
  "scope_note": "Nakahara Definition 4.7：收缩映射。完整条件以所列原文节点为准；不将同框中作为前提提及的概念视为被定义。",
  "identity_status": "active",
  "identity_revision": "94e58841f2dbbf29ed3cf634498dcb69806b696e6664d651f732749fc04ec38f",
  "occurrences": [
    {
      "concept_id": "urn:uuid:60b34861-2f0d-55d9-870b-0057366b7436",
      "book_id": "nakahara-geometry-topology-physics",
      "edition_id": "second-edition-local",
      "lang": "zh-CN",
      "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/02-section-4-2",
      "anchor": "bound-first-f647cf7af93876b9884bd9d3",
      "chapter": "4",
      "section": "4.2",
      "offset": 29729,
      "range": [
        42606,
        43078
      ],
      "source_revision": "0d2ea865f77644f0a36813a8be1649b04b854d432ffad5c714d2fa7e0b31fb3a",
      "source_category": "machine_draft",
      "review_status": "unreviewed",
      "role": "first-mention",
      "role_basis": {
        "kind": "explicit-source-uuid-marker",
        "source_bound_role": "first-mention",
        "first_mention": true,
        "source_node": "cap-12d3ec08d5dd8a4c2cf22a5a",
        "source_sidecar": {
          "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/provenance/chapter-04/concept-annotations.json",
          "sha256": "d5e62dfb62385102900f839c1162f627e780f8e168759526961482268ef49ac4",
          "page": "4.2",
          "annotation_count": 46,
          "policy": "explicit-source-bound-UUIDs; no string-based identity allocation",
          "rendered_annotation_count": 28,
          "plain_mention_count": 18,
          "display_policy": "clickable-only"
        }
      },
      "label": "收缩映射",
      "context": {
        "range": [
          40584,
          43086
        ],
        "quote": null,
        "quote_sha256": "364eb5427ff574b97a9183322e34a8030b71b0cd5fe422457c4c8ec871123ad3",
        "environment": null,
        "excerpt_omitted": true
      },
      "parallel_readings": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-04/02-section-4-2",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-2af8319d44eca1862f8ad8e5"
    },
    {
      "concept_id": "urn:uuid:60b34861-2f0d-55d9-870b-0057366b7436",
      "book_id": "nakahara-geometry-topology-physics",
      "edition_id": "second-edition-local",
      "lang": "zh-CN",
      "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/10-section-4-10",
      "anchor": "bound-mention-ba0417601fc13e4b70138643",
      "chapter": "4",
      "section": "4.10",
      "offset": 43838,
      "range": [
        56117,
        56752
      ],
      "source_revision": "4f858934af0bab2619bf30d7a30d09fe0143da86ee42d9ffc371e87f8940ff70",
      "source_category": "machine_draft",
      "review_status": "unreviewed",
      "role": "discussion",
      "role_basis": {
        "kind": "explicit-source-uuid-marker",
        "source_bound_role": "discussion",
        "first_mention": false,
        "source_node": "a-7fa85ed46b32366541580f0b",
        "source_sidecar": {
          "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/provenance/chapter-04/concept-annotations.json",
          "sha256": "d5e62dfb62385102900f839c1162f627e780f8e168759526961482268ef49ac4",
          "page": "4.10",
          "annotation_count": 68,
          "policy": "explicit-source-bound-UUIDs; no string-based identity allocation",
          "rendered_annotation_count": 21,
          "plain_mention_count": 47,
          "display_policy": "clickable-only"
        }
      },
      "label": "收缩映射",
      "context": {
        "range": [
          51772,
          56757
        ],
        "quote": null,
        "quote_sha256": "b8f4f856523727011e0f8fcc5a20df635e2b9333a65f9bae8f357fa9b0323809",
        "environment": null,
        "excerpt_omitted": true
      },
      "parallel_readings": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-04/10-section-4-10",
          "lang": "en",
          "source_category": "machine_draft",
          "basis": "registered-book-edition-section-language-context; not-concept-equivalence"
        }
      ],
      "id": "occ-f70c550090905d2986f33ddd"
    }
  ],
  "registered_positions": [],
  "statements": [],
  "resolved_references": [
    {
      "raw": "href=\"02-section-4-2.md#bound-definition-fc0182bb5e75362cea74667e\"",
      "href": "02-section-4-2.md#bound-definition-fc0182bb5e75362cea74667e",
      "range": [
        41674,
        41740
      ],
      "relation": "references",
      "target_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/02-section-4-2",
      "target_anchor": "bound-definition-fc0182bb5e75362cea74667e",
      "resolved": true,
      "reason": null,
      "source_revision": "0d2ea865f77644f0a36813a8be1649b04b854d432ffad5c714d2fa7e0b31fb3a",
      "source_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/02-section-4-2",
      "occurrence_id": "occ-2af8319d44eca1862f8ad8e5"
    },
    {
      "raw": "href=\"10-section-4-10.md#exercise-4-11\"",
      "href": "10-section-4-10.md#exercise-4-11",
      "range": [
        51814,
        51853
      ],
      "relation": "references",
      "target_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/10-section-4-10",
      "target_anchor": "exercise-4-11",
      "resolved": true,
      "reason": null,
      "source_revision": "4f858934af0bab2619bf30d7a30d09fe0143da86ee42d9ffc371e87f8940ff70",
      "source_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/10-section-4-10",
      "occurrence_id": "occ-f70c550090905d2986f33ddd"
    },
    {
      "raw": "[4.8 节](08-section-4-8.md#section-4-8)",
      "href": "08-section-4-8.md#section-4-8",
      "range": [
        52424,
        52462
      ],
      "relation": "references",
      "target_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/08-section-4-8",
      "target_anchor": "section-4-8",
      "resolved": true,
      "reason": null,
      "source_revision": "4f858934af0bab2619bf30d7a30d09fe0143da86ee42d9ffc371e87f8940ff70",
      "source_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/10-section-4-10",
      "occurrence_id": "occ-f70c550090905d2986f33ddd"
    },
    {
      "raw": "[图 4.20](08-section-4-8.md#figure-4-20)",
      "href": "08-section-4-8.md#figure-4-20",
      "range": [
        53582,
        53621
      ],
      "relation": "references",
      "target_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/08-section-4-8",
      "target_anchor": "figure-4-20",
      "resolved": true,
      "reason": null,
      "source_revision": "4f858934af0bab2619bf30d7a30d09fe0143da86ee42d9ffc371e87f8940ff70",
      "source_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/10-section-4-10",
      "occurrence_id": "occ-f70c550090905d2986f33ddd"
    },
    {
      "raw": "href=\"02-section-4-2.md#bound-definition-7d3a7d46b3978c1b290931f4\"",
      "href": "02-section-4-2.md#bound-definition-7d3a7d46b3978c1b290931f4",
      "range": [
        55185,
        55251
      ],
      "relation": "references",
      "target_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/02-section-4-2",
      "target_anchor": "bound-definition-7d3a7d46b3978c1b290931f4",
      "resolved": true,
      "reason": null,
      "source_revision": "4f858934af0bab2619bf30d7a30d09fe0143da86ee42d9ffc371e87f8940ff70",
      "source_route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/10-section-4-10",
      "occurrence_id": "occ-f70c550090905d2986f33ddd"
    }
  ],
  "reading_order": [
    "occ-2af8319d44eca1862f8ad8e5",
    "occ-f70c550090905d2986f33ddd"
  ],
  "recorded_dependencies": [],
  "reading_paths": [],
  "coverage": {
    "registered_positions": 0,
    "located_occurrences": 2,
    "whole_book_search_complete": false,
    "registered_positions_truncated": false,
    "independent_human_review_implied": false
  },
  "unresolved": [],
  "reviewed_definitions": [
    {
      "concept_id": "urn:uuid:60b34861-2f0d-55d9-870b-0057366b7436",
      "definition_id": "urn:uuid:7a6caa5c-0ac9-5e9d-8e31-c32d3c86d6ce",
      "definition_group": "definition-4-7",
      "path": "library/concepts/source-evidence/mcp/71fc685dbea97fa32b8f7390f30aa8648b078a875039b49ab03a81a8032e0af0.txt",
      "range": [
        0,
        217
      ],
      "quote": "Definition 4.7. Let  $R$  ( $\\neq \\emptyset$ ) be a subspace of  $X$ . If there exists a continuous map  $f: X \\to R$  such that  $f|_{R} = \\mathrm{id}_{R}$ ,  $R$  is called a retract of  $X$  and  $f$  a retraction.",
      "document_sha256": "71fc685dbea97fa32b8f7390f30aa8648b078a875039b49ab03a81a8032e0af0",
      "quote_sha256": "71fc685dbea97fa32b8f7390f30aa8648b078a875039b49ab03a81a8032e0af0",
      "book_id": "nakahara-geometry-topology-physics",
      "edition_id": "second-edition-local",
      "scope": {
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "source_id": "nakahara-mineru-bd76b709"
      },
      "section": "4.2.2",
      "pdf_page_index": 147,
      "node": "a-465eb9f0639ecf67d34f9b46",
      "source_node_sha256": "71fc685dbea97fa32b8f7390f30aa8648b078a875039b49ab03a81a8032e0af0",
      "upstream": {
        "path": "library/concepts/source-evidence/mcp/b3b8786a55998342d81298441d5b1ee04599bb74680a8e7994c182b1a358720a.json",
        "document_sha256": "b3b8786a55998342d81298441d5b1ee04599bb74680a8e7994c182b1a358720a",
        "node_id": "a-465eb9f0639ecf67d34f9b46",
        "node_source_sha256": "71fc685dbea97fa32b8f7390f30aa8648b078a875039b49ab03a81a8032e0af0"
      },
      "conditions": "Nakahara Definition 4.7：收缩映射。完整条件以所列原文节点为准；不将同框中作为前提提及的概念视为被定义。",
      "review_status": "librarian-original-source-reviewed",
      "source_locator": {
        "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/chapter-04.yaml",
        "sha256": "686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb",
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "nodes": [
          "a-465eb9f0639ecf67d34f9b46",
          "a-ae5a3b14baea57cfcc306149"
        ],
        "node_hashes": {
          "a-465eb9f0639ecf67d34f9b46": "71fc685dbea97fa32b8f7390f30aa8648b078a875039b49ab03a81a8032e0af0",
          "a-ae5a3b14baea57cfcc306149": "ea08d98477d0944e353e5f6096d7ad8ed6fec4c65e0ecdb62d3601534679cf7d"
        },
        "environment": "definition-4-7"
      },
      "environment_basis": {
        "path": "library/concepts/source-evidence/environment-basis/686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb.yaml.txt",
        "document_sha256": "686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb",
        "source_path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/chapter-04.yaml"
      },
      "role": "definition",
      "first_in_book": "not-established",
      "evidence_origin": "explicit-reviewed-source-manifest",
      "definition_part": "definition-environment",
      "definition_part_basis": "original-environment-range",
      "reading_links": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-04/02-section-4-2",
          "anchor": "node-a-465eb9f0639ecf67d34f9b46",
          "lang": "en",
          "basis": "explicit-source-anchor"
        },
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/02-section-4-2",
          "anchor": "node-a-465eb9f0639ecf67d34f9b46",
          "lang": "zh-CN",
          "basis": "explicit-source-anchor"
        }
      ]
    },
    {
      "concept_id": "urn:uuid:60b34861-2f0d-55d9-870b-0057366b7436",
      "definition_id": "urn:uuid:7a6caa5c-0ac9-5e9d-8e31-c32d3c86d6ce",
      "definition_group": "definition-4-7",
      "path": "library/concepts/source-evidence/mcp/ea08d98477d0944e353e5f6096d7ad8ed6fec4c65e0ecdb62d3601534679cf7d.txt",
      "range": [
        0,
        134
      ],
      "quote": "Note that the whole of  $X$  is mapped onto  $R$  keeping points in  $R$  fixed. Figure 4.7 is an example of a retract and retraction.",
      "document_sha256": "ea08d98477d0944e353e5f6096d7ad8ed6fec4c65e0ecdb62d3601534679cf7d",
      "quote_sha256": "ea08d98477d0944e353e5f6096d7ad8ed6fec4c65e0ecdb62d3601534679cf7d",
      "book_id": "nakahara-geometry-topology-physics",
      "edition_id": "second-edition-local",
      "scope": {
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "source_id": "nakahara-mineru-bd76b709"
      },
      "section": "4.2.2",
      "pdf_page_index": 147,
      "node": "a-ae5a3b14baea57cfcc306149",
      "source_node_sha256": "ea08d98477d0944e353e5f6096d7ad8ed6fec4c65e0ecdb62d3601534679cf7d",
      "upstream": {
        "path": "library/concepts/source-evidence/mcp/b3b8786a55998342d81298441d5b1ee04599bb74680a8e7994c182b1a358720a.json",
        "document_sha256": "b3b8786a55998342d81298441d5b1ee04599bb74680a8e7994c182b1a358720a",
        "node_id": "a-ae5a3b14baea57cfcc306149",
        "node_source_sha256": "ea08d98477d0944e353e5f6096d7ad8ed6fec4c65e0ecdb62d3601534679cf7d"
      },
      "conditions": "Nakahara Definition 4.7：收缩映射。完整条件以所列原文节点为准；不将同框中作为前提提及的概念视为被定义。",
      "review_status": "librarian-original-source-reviewed",
      "source_locator": {
        "path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/chapter-04.yaml",
        "sha256": "686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb",
        "book_id": "nakahara-geometry-topology-physics",
        "edition_id": "second-edition-local",
        "nodes": [
          "a-465eb9f0639ecf67d34f9b46",
          "a-ae5a3b14baea57cfcc306149"
        ],
        "node_hashes": {
          "a-465eb9f0639ecf67d34f9b46": "71fc685dbea97fa32b8f7390f30aa8648b078a875039b49ab03a81a8032e0af0",
          "a-ae5a3b14baea57cfcc306149": "ea08d98477d0944e353e5f6096d7ad8ed6fec4c65e0ecdb62d3601534679cf7d"
        },
        "environment": "definition-4-7"
      },
      "environment_basis": {
        "path": "library/concepts/source-evidence/environment-basis/686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb.yaml.txt",
        "document_sha256": "686a132664d165624b3568926e3cb3ac1d45c7d04a4c28bef749b47a557e01bb",
        "source_path": "library/books/nakahara-geometry-topology-physics/second-edition-local/chapters/chapter-04.yaml"
      },
      "role": "definition",
      "first_in_book": "not-established",
      "evidence_origin": "explicit-reviewed-source-manifest",
      "definition_part": "continuation",
      "definition_part_basis": "original-environment-range",
      "reading_links": [
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/en/chapter-04/02-section-4-2",
          "anchor": "node-a-ae5a3b14baea57cfcc306149",
          "lang": "en",
          "basis": "explicit-source-anchor"
        },
        {
          "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/02-section-4-2",
          "anchor": "node-a-ae5a3b14baea57cfcc306149",
          "lang": "zh-CN",
          "basis": "explicit-source-anchor"
        }
      ]
    }
  ],
  "part_of_speech": "noun",
  "base_revision": "b43629e9733d5798b14f045b5660c76beb915799fb39dc0e5b92fee16e0be3c4",
  "optional_enrichments": []
}