| dc.creator | Bhardwaj, Manoj | |
| dc.creator | Osipov, Alexander V. | |
| dc.date | 2023-07-19 | |
| dc.date.accessioned | 2023-12-19T18:55:51Z | |
| dc.date.available | 2023-12-19T18:55:51Z | |
| dc.identifier | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3417 | |
| dc.identifier | 10.56754/0719-0646.2502.161 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/239183 | |
| dc.description | In this paper, we prove that a clopen version \(S_1(\mathcal{C}_\mathcal{O}, \mathcal{C}_\mathcal{O})\) of the Rothberger property and Borel strong measure zeroness are independent. For a zero-dimensional metric space \((X,d)\), \(X\) satisfies \(S_1(\mathcal{C}_\mathcal{O}, \mathcal{C}_\mathcal{O})\) if, and only if, \(X\) has Borel strong measure zero with respect to each metric which has the same topology as \(d\) has. In a zero-dimensional space, the game \(G_1(\mathcal{O}, \mathcal{O})\) is equivalent to the game \(G_1(\mathcal{C}_\mathcal{O}, \mathcal{C}_\mathcal{O})\) and the point-open game is equivalent to the point-clopen game. Using reflections, we obtain that the game \(G_1(\mathcal{C}_\mathcal{O}, \mathcal{C}_\mathcal{O})\) and the point-clopen game are strategically and Markov dual. An example is given for a space on which the game \(G_1(\mathcal{C}_\mathcal{O}, \mathcal{C}_\mathcal{O})\) is undetermined. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
| dc.relation | https://cubo.ufro.cl/ojs/index.php/cubo/article/view/3417/2296 | |
| dc.rights | Copyright (c) 2023 Manoj Bhardwaj et al. | en-US |
| dc.rights | https://creativecommons.org/licenses/by-nc/4.0/ | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 25 No. 2 (2023); 161–172 | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 25 No. 2 (2023); 161–172 | es-ES |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.subject | Strong measure zero | en-US |
| dc.subject | selection principles | en-US |
| dc.subject | point-clopen game | en-US |
| dc.subject | zero-dimensional space | en-US |
| dc.subject | 54D20 | en-US |
| dc.subject | 54A20 | en-US |
| dc.title | Some observations on a clopen version of the Rothberger property | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
