Uniform density and m -density for subrings of C(X
| dc.contributor.author | Garrido, M. Isabel | |
| dc.contributor.author | Montalvo, Francisco | |
| dc.date.accessioned | 2023-06-20T18:45:53Z | |
| dc.date.available | 2023-06-20T18:45:53Z | |
| dc.date.issued | 1994 | |
| dc.description.abstract | Let C(X) denote the continuous real-valued functions on a topological space X . The question of whether a u -dense subring of C(X) is m -dense is studied in this note. Recall that neighborhoods of a function f in the u -topology are determined by an interval (f−ε,f+ε) for ε a positive number and in the m -topology by intervals (f−e,f+e) for u a positive unit in C(X) . J. Kurzweil [Studia Math. 14 (1954), 214–231, had shown that u -denseness and m -denseness are equivalent for subrings of C(X) closed under bounded inversion. Here, the authors prove that this result is not valid for arbitrary subrings of C(X) . In particular, they show that the property of every u -dense subring being m -dense is equivalent to X being pseudocompact | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21707 | |
| dc.identifier.issn | 0213-8743 | |
| dc.identifier.officialurl | http://dmle.cindoc.csic.es/pdf/EXTRACTAMATHEMATICAE_1994_09_01_07.pdf | |
| dc.identifier.relatedurl | http://www.eweb.unex.es/eweb/extracta/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58544 | |
| dc.issue.number | 1 | |
| dc.journal.title | Extracta Mathematicae | |
| dc.language.iso | eng | |
| dc.page.final | 50 | |
| dc.page.initial | 48 | |
| dc.publisher | Universidad de Extremadura, Departamento de Matemáticas | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.1 | |
| dc.subject.keyword | u-dense subring | |
| dc.subject.keyword | m-dense | |
| dc.subject.ucm | Topología | |
| dc.subject.unesco | 1210 Topología | |
| dc.title | Uniform density and m -density for subrings of C(X | |
| dc.type | journal article | |
| dc.volume.number | 9 | |
| dspace.entity.type | Publication |
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