{"paper":{"title":"Locally Constant Functions","license":"","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Joan Hart, Kenneth Kunen","submitted_at":"1995-05-08T00:00:00Z","abstract_excerpt":"Let X be a compact Hausdorff space and M a metric space. E_0(X,M) is the set of f in C(X,M) such that there is a dense set of points x in X with f constant on some neighborhood of x. We describe some general classes of X for which E_0(X,M) is all of C(X,M). These include beta N - N, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case that M is a Banach space, we discuss the properties of E_0(X,M) as a normed linear space. We also build three first countable Eberlein compact spaces, F,G,H, with various E_0 properties: For all metric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9505204","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"}