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We prove that $M(H^\\infty)$ is homeomorphic to the Freudenthal compactification $\\gamma(M_a)$ of the set $M_a$ of all non-trivial (analytic disks) Gleason parts of $M(H^\\infty)$. Also, we give alternative proofs of important results of Su\\'{a}rez asserting that the set $M_s$ of trivial (one-pointed) Gleason parts of $M(H^\\infty)$ is totally disconnected and that the \\v{C}ech cohomology group $H^2(M(H^\\infty),\\mathbb Z)=0$."},"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":"1507.03669","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-14T00:50:09Z","cross_cats_sorted":[],"title_canon_sha256":"bdcaaf1da098fad095154f26735a0e8f151136b3a31141d6e24bbbf37f678c39","abstract_canon_sha256":"26d85307a728f6f4a040b006be4b8bcb762f3d9fc025f3096aa4e987f4b5bc85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:57.658680Z","signature_b64":"baXr190rl+mEl+rsW0F8/n7JCshUM5RWYcK5WnL1U/uWgMk5JDqaiOmOiXuwkkNokHsYlQvexad5PGZzzbi+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dcfde7501af038bec18002eab44e1aa39e16e1d9dc458f1690273ca16af4450","last_reissued_at":"2026-05-18T01:36:57.658021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:57.658021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Topology of the Maximal Ideal Space of $H^\\infty$ Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexander Brudnyi","submitted_at":"2015-07-14T00:50:09Z","abstract_excerpt":"Let $M(H^\\infty)$ be the maximal ideal space of the Banach algebra $H^\\infty$ of bounded holomorphic functions on the unit disk $\\mathbb D\\subset\\mathbb C$. 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