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Here are the main results of the paper:\n  Theorem: If $\\{K_s\\}_{s\\in S}$ is a family of pointed quasi-finite complexes, then their wedge $\\bigvee\\limits_{s\\in S}K_s$ is quasi-finite.\n  Theorem: If $K_1$ and $K_2$ are quasi-finite countable complexes, then their join $K_1\\ast K_2$ is quasi-finite.\n  Theorem: For every quasi-finite CW complex $K$ there is a family $\\{K_s\\}_{s\\in S}$ of countable CW complexes such that $\\bigvee\\limits_{s\\in S} K"},"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":"math/0608748","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2006-08-30T08:30:26Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"2c43f84bfb0457a4308a58638f79cfeaef40e0773dc5e88649e2a58c39f0b964","abstract_canon_sha256":"0f1294064a75eee0f8f667c5a53444dba0aed1bb8163b5a133260ddde150ed5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:46.720916Z","signature_b64":"TdFyTBY4SSRJHwj0/45vraqD+vt+Ge4GrXmqQcdyFkWoHFu0a3DRuofTVr4+vedjnyZ/HpQ/2SxlQQZngI/tAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a80c78bceea05e3826e0e59be9b4a14c7324fdb15ecaf9aaccc5963a32e5adb","last_reissued_at":"2026-05-18T00:08:46.720360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:46.720360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Compact maps and quasi-finite complexes","license":"","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"A. 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