{"paper":{"title":"Openly factorizable spaces and compact extensions of topological semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"Svetlana Dimitrova, Taras Banakh","submitted_at":"2008-11-26T11:22:05Z","abstract_excerpt":"We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its the Stone-\\v{C}ech compactification $\\beta S$ provided $S$ is a pseudocompact openly factorizable space, which means that each map $f:S\\to Y$ to a second countable space $Y$ can be written as the composition $f=g\\circ p$ of an open map $p:X\\to Z$ onto a second countable space $Z$ and a map $g:Z\\to Y$. We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.4272","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"}