{"paper":{"title":"Some new results on functions in $C(X)$ having their support on ideals of closed sets","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Goutam Bhunia, Pritam Rooj, Sagarmoy Bag, Sudip Kumar Acharyya","submitted_at":"2017-12-28T10:51:37Z","abstract_excerpt":"For any ideal $\\mathcal{P}$ of closed sets in $X$, let $C_\\mathcal{P}(X)$ be the family of those functions in $C(X)$ whose support lie on $\\mathcal{P}$. Further let $C^\\mathcal{P}_\\infty(X)$ contain precisely those functions $f$ in $C(X)$ for which for each $\\epsilon >0, \\{x\\in X: \\lvert f(x)\\rvert\\geq \\epsilon\\}$ is a member of $\\mathcal{P}$. Let $\\upsilon_{C_{\\mathcal{P}}}X$ stand for the set of all those points $p$ in $\\beta X$ at which the stone extension $f^*$ for each $f$ in $C_\\mathcal{P}(X)$ is real valued. We show that each realcompact space lying between $X$ and $\\beta X$ is of the f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09820","kind":"arxiv","version":1},"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"}