{"paper":{"title":"More smoothly real compact spaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Kriegl, Peter W. Michor","submitted_at":"1992-06-01T00:00:00Z","abstract_excerpt":"A topological space $X$ is called $\\Cal A$-real compact, if every algebra homomorphism from $\\Cal A$ to the reals is an evaluation at some point of $X$, where $\\Cal A$ is an algebra of continuous functions. Our main interest lies on algebras of smooth functions. In \\cite{AdR} it was shown that any separable Banach space is smoothly real compact. Here we generalize this result to a huge class of locally convex spaces including arbitrary products of separable Fr\\'echet spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9206204","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"}