{"paper":{"title":"Extension properties of Stone-\\v{C}ech coronas and proper absolute extensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"A. Chigogidze","submitted_at":"2012-08-14T11:16:30Z","abstract_excerpt":"We characterize, in terms of $X$, extensional dimension of the Stone-\\v{C}ech corona $\\beta X \\setminus X$ of locally compact and Lindel\\\"{o}f space $X$. The non-Lindel\\\"{o}f case case is also settled in terms of extending proper maps with values in $I^{\\tau}\\setminus L$, where $L$ is a finite complex. Further, for a finite complex $L$, an uncountable cardinal $\\tau$ and a $Z_{\\tau}$-set $X$ in the Tychonov cube $I^{\\tau}$ we find necessary and sufficient condition, in terms of $I^{\\tau}\\setminus X$, for $X$ to be in the class $\\operatorname{AE}([L])$. We also introduce a concept of a proper a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2829","kind":"arxiv","version":2},"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"}