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A topological space $X$ is called a generalized ordered space (GO-space) whenever $X$ is topologically embeddable in a LOTS. Main Theorem: Let $X$ be a Hausdorff topological space. Assume that any continuous image of $X$ is a GO-space. Then $X$ is homeomorphic to a countable successor ordinal (with the order topology).\n  The converse t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.05271","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2016-05-17T18:10:04Z","cross_cats_sorted":[],"title_canon_sha256":"6a0f71750c1c092ea094e4783a724507414e2d88ce9b883e00728bd7e058c815","abstract_canon_sha256":"66b1fccf6c0786bac83c0481682d4c65b3c4c519f37dcba9bf3a5b1e1b4386e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:40.265981Z","signature_b64":"M3xp6x/wPGV4+AZ1cgXzVl3D62eI6EQThwvrxhkU2F29aZaj/Gy2oNAchiFnTnSbfXHE6T+bb5g6NoSQ/NZJAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7114c071aa0cf431ecc35e1de6c911d7805a12e0f3240c27e52407b18d22fa6","last_reissued_at":"2026-05-18T00:53:40.265491Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:40.265491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Countable Successor Ordinals as Generalized Ordered Topological Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Arkady Leiderman, Robert Bonnet","submitted_at":"2016-05-17T18:10:04Z","abstract_excerpt":"A topological space $L$ is called a linear ordered topological space (LOTS) whenever there is a linear order $\\leq$ on $L$ such that the topology on $L$ is generated by the open sets of the form $(a, b)$ with $a < b$ and $a, b \\in L \\cup \\{ -\\infty, +\\infty \\}$. A topological space $X$ is called a generalized ordered space (GO-space) whenever $X$ is topologically embeddable in a LOTS. Main Theorem: Let $X$ be a Hausdorff topological space. Assume that any continuous image of $X$ is a GO-space. Then $X$ is homeomorphic to a countable successor ordinal (with the order topology).\n  The converse t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05271","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.05271","created_at":"2026-05-18T00:53:40.265590+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05271v2","created_at":"2026-05-18T00:53:40.265590+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05271","created_at":"2026-05-18T00:53:40.265590+00:00"},{"alias_kind":"pith_short_12","alias_value":"W4IUYBY2UDHU","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"W4IUYBY2UDHUGHWM","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"W4IUYBY2","created_at":"2026-05-18T12:30:48.956258+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/W4IUYBY2UDHUGHWMGXQ543ERDV","json":"https://pith.science/pith/W4IUYBY2UDHUGHWMGXQ543ERDV.json","graph_json":"https://pith.science/api/pith-number/W4IUYBY2UDHUGHWMGXQ543ERDV/graph.json","events_json":"https://pith.science/api/pith-number/W4IUYBY2UDHUGHWMGXQ543ERDV/events.json","paper":"https://pith.science/paper/W4IUYBY2"},"agent_actions":{"view_html":"https://pith.science/pith/W4IUYBY2UDHUGHWMGXQ543ERDV","download_json":"https://pith.science/pith/W4IUYBY2UDHUGHWMGXQ543ERDV.json","view_paper":"https://pith.science/paper/W4IUYBY2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05271&json=true","fetch_graph":"https://pith.science/api/pith-number/W4IUYBY2UDHUGHWMGXQ543ERDV/graph.json","fetch_events":"https://pith.science/api/pith-number/W4IUYBY2UDHUGHWMGXQ543ERDV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W4IUYBY2UDHUGHWMGXQ543ERDV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W4IUYBY2UDHUGHWMGXQ543ERDV/action/storage_attestation","attest_author":"https://pith.science/pith/W4IUYBY2UDHUGHWMGXQ543ERDV/action/author_attestation","sign_citation":"https://pith.science/pith/W4IUYBY2UDHUGHWMGXQ543ERDV/action/citation_signature","submit_replication":"https://pith.science/pith/W4IUYBY2UDHUGHWMGXQ543ERDV/action/replication_record"}},"created_at":"2026-05-18T00:53:40.265590+00:00","updated_at":"2026-05-18T00:53:40.265590+00:00"}