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The following are the main results of the paper: (i) If $X$ is a Peano continuum then $AC(X,x)$ is a cell-like Peano continuum; (ii) If $X$ is $n-$dimensional then $AC(X, x)$ is $(n+1)-$dimensional; and (iii) For a path connected space $X$, $\\pi_1(X,x)$ is trivial if and only if $\\pi_2(AC(X, x))$ is trivial. As a corollary, $AC(S^1, x)$ is a 2-dimensional nonaspherical cell-like Peano continuum."},"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":"1302.4124","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-17T21:43:27Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"3dd2b283a4a8a7be85cd9d86b0437cd27e139a863745b94d50aac56e6c050cf4","abstract_canon_sha256":"0411a91220bd532d0a6fb6631f5fca8738c1bc6d7e8120ff16bc01ed68749f7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:24.068259Z","signature_b64":"5qE8r2zJgDCqG3+mCA4RHN+oEW+KDDkv1ICPajn/7vlypczErqRcy/gdxExTXGy5GRXsSQAOEQwSs2Ro+In6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2388dab9875fb3f9e948562171cfbb3d703db930b5324706d9dee19ba8e76029","last_reissued_at":"2026-05-18T03:33:24.067764Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:24.067764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On 2-dimensional nonaspherical cell-like Peano continua: A simplified approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GT","authors_text":"Du\\v{s}an Repov\\v{s}, Katsuya Eda, Umed H. Karimov","submitted_at":"2013-02-17T21:43:27Z","abstract_excerpt":"We construct a functor $AC(-,-)$ from the category of path connected spaces $X$ with a base point $x$ to the category of simply connected spaces. The following are the main results of the paper: (i) If $X$ is a Peano continuum then $AC(X,x)$ is a cell-like Peano continuum; (ii) If $X$ is $n-$dimensional then $AC(X, x)$ is $(n+1)-$dimensional; and (iii) For a path connected space $X$, $\\pi_1(X,x)$ is trivial if and only if $\\pi_2(AC(X, x))$ is trivial. 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