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0. 1 + n, x _ {0} + 0. 1 + n)\n$$\n", "document_sha256": "136ce4ffa911673d7563d287c20fdb6737aa13c84a38796538290381e5d7aaf2", "quote_sha256": "136ce4ffa911673d7563d287c20fdb6737aa13c84a38796538290381e5d7aaf2", "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": "4.6.5", "pdf_page_index": 167, "node": "a-c2fb5f740fad7197d0b031a8", "source_node_sha256": "136ce4ffa911673d7563d287c20fdb6737aa13c84a38796538290381e5d7aaf2", "upstream": { "path": "library/concepts/source-evidence/mcp/4d9ca2583e4e7951272816a56774b349efde92aeba2a2680a39567e1c81b9e10.json", "document_sha256": "4d9ca2583e4e7951272816a56774b349efde92aeba2a2680a39567e1c81b9e10", "node_id": "a-c2fb5f740fad7197d0b031a8", "node_source_sha256": "136ce4ffa911673d7563d287c20fdb6737aa13c84a38796538290381e5d7aaf2" }, "conditions": "Nakahara Definition 4.12：覆叠空间。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-050580e71ece4ae556fbb431", "a-cba560008ac518fab8461493", "a-f93e176dae385677718561c6", "a-d85fb951e7230a294e052a79", "a-c2fb5f740fad7197d0b031a8", "a-de9495c9b20c91aea0cf453a" ], "node_hashes": { "a-050580e71ece4ae556fbb431": "db6ae9484c3a14f0c05fe66f60ccb5a1012fda72716f24bb567eada70938985a", "a-cba560008ac518fab8461493": "82e7884af77df0e8469301210807245fa6251c96239d6a9f2ebb5d5cb6817ed2", "a-f93e176dae385677718561c6": "729a0e6b937db3ed67fab46cc5007ed30f2a9ee78d10ebc0672ac725fc4265e7", "a-d85fb951e7230a294e052a79": "8e10aecbf1ab485ec7cb160b4ef7fb635a7bcb2b71722b9a8aabfc4e8ea2a5db", "a-c2fb5f740fad7197d0b031a8": "136ce4ffa911673d7563d287c20fdb6737aa13c84a38796538290381e5d7aaf2", "a-de9495c9b20c91aea0cf453a": "d08f3cd44ab6959e35a7d33e8eb50b96136d83f385d267ec6cabac9af804901a" }, "environment": "definition-4-12" }, "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-04/06-section-4-6", "anchor": "node-a-c2fb5f740fad7197d0b031a8", "lang": "en", "basis": "explicit-source-anchor" }, { "route": "books/nakahara-geometry-topology-physics/second-edition-local/zh/chapter-04/06-section-4-6", "anchor": "node-a-c2fb5f740fad7197d0b031a8", "lang": "zh-CN", "basis": "explicit-source-anchor" } ] }, { "concept_id": "urn:uuid:980eae96-7af8-5311-a7e2-f65c0020e8c6", "definition_id": "urn:uuid:a1a4e92d-07b6-5eb2-a565-dfe53267e70a", "definition_group": "definition-4-12", "path": "library/concepts/source-evidence/mcp/d08f3cd44ab6959e35a7d33e8eb50b96136d83f385d267ec6cabac9af804901a.txt", "range": [ 0, 281 ], "quote": "which is a disjoint union of open sets of $\\mathbb{R}$ . It is easy to show that $p$ is also a homomorphism with respect to addition in $\\mathbb{R}$ and multiplication in $\\mathrm{U}(1)$ . 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