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Dostęp zamkniętyA countable dense homogeneous topological vector space is a Baire space
| dc.abstract.en | We prove that every homogeneous countable dense homogeneous topological space containing a copy of the Cantor set is a Baire space. In particular, every countable dense homogeneous topological vector space is a Baire space. It follows that, for any nondiscrete metrizable space , the function space is not countable dense homogeneous. This answers a question posed recently by R. Hernández-Gutiérrez. We also conclude that, for any infinite-dimensional Banach space (dual Banach space ), the space equipped with the weak topology ( with the weak topology) is not countable dense homogeneous. We generalize some results of Hrušák, Zamora Avilés, and Hernández-Gutiérrez concerning countable dense homogeneous products. |
| dc.affiliation | Uniwersytet Warszawski |
| dc.contributor.author | Krupski, Mikołaj |
| dc.contributor.author | Dobrowolski, Tadeusz |
| dc.contributor.author | Marciszewski, Witold |
| dc.date.accessioned | 2024-01-24T17:18:31Z |
| dc.date.available | 2024-01-24T17:18:31Z |
| dc.date.issued | 2021 |
| dc.description.finance | Publikacja bezkosztowa |
| dc.description.number | 4 |
| dc.description.volume | 149 |
| dc.identifier.doi | 10.1090/PROC/15271 |
| dc.identifier.issn | 0002-9939 |
| dc.identifier.uri | https://repozytorium.uw.edu.pl//handle/item/101497 |
| dc.identifier.weblink | https://www.ams.org/proc/earlyview/#proc15271/.pdf |
| dc.language | eng |
| dc.pbn.affiliation | mathemathics |
| dc.relation.ispartof | Proceedings of the American Mathematical Society |
| dc.relation.pages | 1773-1789 |
| dc.rights | ClosedAccess |
| dc.sciencecloud | nosend |
| dc.title | A countable dense homogeneous topological vector space is a Baire space |
| dc.type | JournalArticle |
| dspace.entity.type | Publication |