{"paper":{"title":"Arzel\\`a-Ascoli theorem via Wallman compactification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GN","authors_text":"Mateusz Krukowski","submitted_at":"2016-02-18T06:56:57Z","abstract_excerpt":"In the paper, we recall the Wallman compactification of a Tychonoff space $T$ (denoted by $\\text{Wall}(T)$) and the contribution made by Gillman and Jerison. Motivated by the Gelfand-Naimark theorem, we investigate the homeomorphism between $BC(T,\\mathbb{R})$ and $BC(\\text{Wall}(T),\\mathbb{R})$. Along the way, we attempt to justify the advantages of Wallman compactification over other manifestations of Stone-\\v{C}ech compactification. The main result of the paper is a new form of Arzel\\`a-Ascoli theorem, which introduces the concept of equicontinuity along $\\omega$-ultrafilters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05691","kind":"arxiv","version":3},"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"}