{"paper":{"title":"On the size of the fibers of spectral maps induced by semialgebraic embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jose F. Fernando","submitted_at":"2014-03-31T15:46:17Z","abstract_excerpt":"Let ${\\mathcal S}(M)$ be the ring of (continuous) semialgebraic functions on a semialgebraic set $M\\subset{\\mathbb R}^m$ and ${\\mathcal S}^*(M)$ its subring of bounded semialgebraic functions. In this work we compute the size of the fibers of the spectral maps ${\\rm Spec}({\\tt j})_1:{\\rm Spec}({\\mathcal S}(N))\\to{\\rm Spec}({\\mathcal S}(M))$ and ${\\rm Spec}({\\tt j})_2:{\\rm Spec}({\\mathcal S}^*(N))\\to{\\rm Spec}({\\mathcal S}^*(M))$ induced by the inclusion ${\\tt j}:N\\hookrightarrow M$ of a semialgebraic subset $N$ of $M$. The ring ${\\mathcal S}(M)$ can be understood as the localization of ${\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.8059","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"}