{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RF6OQBUFYRUNPYZLNU5ZMI223M","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9869dd84f3ccb7f51b435e0a7743d77a8d7bd85d4143e2a774c7a7ecd29aac0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-05-11T14:22:26Z","title_canon_sha256":"a04e316c71326d7f9cb3a25ccce535e82388bd2d19d2fcdca06ae083555c2c2f"},"schema_version":"1.0","source":{"id":"1105.2203","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2203","created_at":"2026-05-18T04:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2203v2","created_at":"2026-05-18T04:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2203","created_at":"2026-05-18T04:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"RF6OQBUFYRUN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RF6OQBUFYRUNPYZL","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RF6OQBUF","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:5a9fc4cd0bf925781e5d5d71fb24f7cd5beb522ffd474a44704c25d350292186","target":"graph","created_at":"2026-05-18T04:04:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A topological group $X$ is called connected if the only subsets which are both open and closed are the whole space $X$ and the null set $\\emptyset$. A subset of a topological group is connected if the subspace is connected. We say that a subset $A$ of $X$ is $G$-sequentially connected if the only subsets of $A$ which are both $G$-sequentially open and $G$-sequentially closed, with respect to the relative $G$-sequentially open and $G$-sequentially closed subsets of $A$, are open and closed subsets of $A$ are $A$ and the null set, $\\emptyset$. We investigate the impact of changing the definition","authors_text":"Huseyin Cakalli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-05-11T14:22:26Z","title":"Sequential Definitions of Connectedness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2203","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d008fb8407015a7eaf674056de6a293fc316b19d665c4cab0e0ec17fab663e76","target":"record","created_at":"2026-05-18T04:04:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9869dd84f3ccb7f51b435e0a7743d77a8d7bd85d4143e2a774c7a7ecd29aac0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-05-11T14:22:26Z","title_canon_sha256":"a04e316c71326d7f9cb3a25ccce535e82388bd2d19d2fcdca06ae083555c2c2f"},"schema_version":"1.0","source":{"id":"1105.2203","kind":"arxiv","version":2}},"canonical_sha256":"897ce80685c468d7e32b6d3b96235adb37ce8942ae3d95528b7e53174b1744cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"897ce80685c468d7e32b6d3b96235adb37ce8942ae3d95528b7e53174b1744cd","first_computed_at":"2026-05-18T04:04:06.729799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:06.729799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RpUFSR8kZ8Hl29v3RQIgibZBBHMSiusjyNV/9VtpJZi/lf7HA+5tULONBymk9nrcYzlgc2JRyVVVxWcXBRZACw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:06.730252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2203","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d008fb8407015a7eaf674056de6a293fc316b19d665c4cab0e0ec17fab663e76","sha256:5a9fc4cd0bf925781e5d5d71fb24f7cd5beb522ffd474a44704c25d350292186"],"state_sha256":"24ad401aa69c9dc9c6a7f712e4208ba9b31f8c9078974705d1e1ef85eb373f06"}